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Index 1311Yang–Mills theory, 39, 297higher, 127Zamolodchikov metric, 1220Zorn’s lemma, 18
Index 1311Yang–Mills theory, 39, 297higher, 127Zamolodchikov metric, 1220Zorn’s lemma, 18
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APPLIEDDIFFERENTIALGEOMETRYA Modern
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APPLIEDDIFFERENTIALGEOMETRYA Modern
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Dedicated to:Nitya, Atma and Kali
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PrefaceApplied Differential Geometr
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ixAcknowledgmentsThe authors wish t
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Glossary of Frequently Used Symbols
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Glossary of Frequently Used Symbols
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Glossary of Frequently Used Symbols
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ContentsPrefaceGlossary of Frequent
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Contentsxix2.1.5.2 Forces Acting on
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Contentsxxi3.6.3.4 Stokes Theorem a
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Contentsxxiii3.10.3.1 Basis of Lagr
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Contentsxxv3.17 Applied Unorthodox
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Contentsxxvii4.9.8.2 Geometrodynami
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Contentsxxix4.14.7.5 Monopole Conde
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Contentsxxxi5.12.3 Hawking-Penrose
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Contentsxxxiii6.5.2.4 Dimensional R
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Chapter 1IntroductionIn this introd
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Introduction 3Fig. 1.1 The four cha
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Introduction 5• Riemannian manifo
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Introduction 7charts.The atlas cont
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Introduction 9every point has a nei
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Introduction 11of curves include ci
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Introduction 13the variables define
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Introduction 15U i denotes one of t
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Introduction 17which varies smoothl
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Introduction 19interactions.1.1.5.2
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Introduction 21real number. This co
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Introduction 23Such a force is inde
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Introduction 25tons. In this formul
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Introduction 27vector-field are sol
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Introduction 29or simply connected)
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Introduction 311.1.8 Application: A
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Introduction 33theory itself existe
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Introduction 35mediate the forces.
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Introduction 37theory. 50 Fig. 1.3
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Introduction 39to describe a univer
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Introduction 41which have two disti
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Introduction 43first theory can be
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Introduction 45the Casimir effect,
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Introduction 47• External coordin
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Introduction 49a connection-base de
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Chapter 2Technical Preliminaries: T
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Technical Preliminaries: Tensors, A
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Chapter 3Applied Manifold Geometry3
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Applied Manifold Geometry 139where
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Applied Manifold Geometry 141In loc
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Applied Manifold Geometry 143on the
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Applied Manifold Geometry 145exist
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Applied Manifold Geometry 147then E
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Applied Manifold Geometry 1490D man
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Applied Manifold Geometry 151Fig. 3
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Applied Manifold Geometry 153the fo
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Applied Manifold Geometry 155contin
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Applied Manifold Geometry 157In oth
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Applied Manifold Geometry 159scalar
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Applied Manifold Geometry 161where
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Applied Manifold Geometry 1633.6 Te
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Applied Manifold Geometry 165Let ϕ
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Applied Manifold Geometry 1673.6.1.
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Applied Manifold Geometry 169or, if
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Applied Manifold Geometry 171If X i
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Applied Manifold Geometry 173along
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Applied Manifold Geometry 175is dua
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Applied Manifold Geometry 177where
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Applied Manifold Geometry 179(1) α
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Applied Manifold Geometry 181diagra
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Applied Manifold Geometry 183Clearl
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Applied Manifold Geometry 1853.6.3.
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Applied Manifold Geometry 187duces,
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Applied Manifold Geometry 189This i
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Applied Manifold Geometry 191Hodge
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Applied Manifold Geometry 193The in
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Applied Manifold Geometry 195since
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Applied Manifold Geometry 197If a l
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Applied Manifold Geometry 199asGive
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Applied Manifold Geometry 201The co
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Applied Manifold Geometry 203at the
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Applied Manifold Geometry 205For ex
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Applied Manifold Geometry 207axis,
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Applied Manifold Geometry 209For ex
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Applied Manifold Geometry 211The sp
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Applied Manifold Geometry 213corres
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Applied Manifold Geometry 215corres
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Applied Manifold Geometry 217Specia
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Applied Manifold Geometry 219the co
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Applied Manifold Geometry 221moment
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Applied Manifold Geometry 223produc
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Applied Manifold Geometry 225has a
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Applied Manifold Geometry 2273.8.5
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Applied Manifold Geometry 229in whi
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Applied Manifold Geometry 231with
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Applied Manifold Geometry 233itly:(
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Applied Manifold Geometry 235play t
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Applied Manifold Geometry 237Some r
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Applied Manifold Geometry 239Basic
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Applied Manifold Geometry 241orthog
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Applied Manifold Geometry 243is adm
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Applied Manifold Geometry 245Root S
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Applied Manifold Geometry 247groups
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Applied Manifold Geometry 2493.9.1.
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Applied Manifold Geometry 251second
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Applied Manifold Geometry 253where
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Applied Manifold Geometry 255be a v
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Applied Manifold Geometry 257Now, a
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Applied Manifold Geometry 259This i
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Applied Manifold Geometry 2613.9.4
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Applied Manifold Geometry 263other
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Applied Manifold Geometry 265where
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Applied Manifold Geometry 267result
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Applied Manifold Geometry 269where
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Applied Manifold Geometry 2713.10 R
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Applied Manifold Geometry 273More p
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Applied Manifold Geometry 275Y (t 0
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Applied Manifold Geometry 277which
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Applied Manifold Geometry 279for an
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Applied Manifold Geometry 281where
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Applied Manifold Geometry 283Thus w
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Applied Manifold Geometry 2853.10.2
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Applied Manifold Geometry 287evolut
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Applied Manifold Geometry 2893.10.3
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Applied Manifold Geometry 2913.10.3
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Applied Manifold Geometry 293‘ren
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Applied Manifold Geometry 295mute;
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Applied Manifold Geometry 297Rather
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Applied Manifold Geometry 299of the
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Applied Manifold Geometry 301clidea
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Applied Manifold Geometry 303Second
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Applied Manifold Geometry 305i.e.,
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Applied Manifold Geometry 307invari
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Applied Manifold Geometry 309The Ba
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Applied Manifold Geometry 311Let us
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Applied Manifold Geometry 313all cu
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Applied Manifold Geometry 315ders.
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Applied Manifold Geometry 317this c
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Applied Manifold Geometry 319In par
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Applied Manifold Geometry 321As I p
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Applied Manifold Geometry 323the fo
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Applied Manifold Geometry 325per (1
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Applied Manifold Geometry 327Genera
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Applied Manifold Geometry 329The ma
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Applied Manifold Geometry 331pretat
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Applied Manifold Geometry 333byMDL
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Applied Manifold Geometry 3353.12 S
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Applied Manifold Geometry 337H 2 (M
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Applied Manifold Geometry 339bracke
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Applied Manifold Geometry 341Any so
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Applied Manifold Geometry 343All on
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Applied Manifold Geometry 345The ac
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Applied Manifold Geometry 347linear
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Applied Manifold Geometry 349such t
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Applied Manifold Geometry 351Let γ
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Applied Manifold Geometry 353This i
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Applied Manifold Geometry 355chart
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Applied Manifold Geometry 357phase-
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Applied Manifold Geometry 359( ) 0
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Applied Manifold Geometry 361hetero
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Applied Manifold Geometry 363thus c
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Applied Manifold Geometry 365Action
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Applied Manifold Geometry 367and we
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Applied Manifold Geometry 369action
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Applied Manifold Geometry 371and we
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Applied Manifold Geometry 373by (J(
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Applied Manifold Geometry 375fields
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Applied Manifold Geometry 377Let Tx
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Applied Manifold Geometry 379where
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Applied Manifold Geometry 381The ve
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Applied Manifold Geometry 383and gi
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Applied Manifold Geometry 385The co
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Applied Manifold Geometry 387tor Ca
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Applied Manifold Geometry 389where
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Applied Manifold Geometry 3912 −
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Applied Manifold Geometry 393comple
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Applied Manifold Geometry 395F[C]
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Applied Manifold Geometry 397become
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Applied Manifold Geometry 399of fuz
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Applied Manifold Geometry 401In our
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Applied Manifold Geometry 403Biodyn
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Applied Manifold Geometry 405for T
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Applied Manifold Geometry 407A vari
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Applied Manifold Geometry 409such t
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Applied Manifold Geometry 411of neg
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Applied Manifold Geometry 413where
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Applied Manifold Geometry 415Follow
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Applied Manifold Geometry 417and J
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Applied Manifold Geometry 419This t
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Applied Manifold Geometry 421above,
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Applied Manifold Geometry 423As a L
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Applied Manifold Geometry 425Theore
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Applied Manifold Geometry 427real v
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Applied Manifold Geometry 429indepe
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Applied Manifold Geometry 431In ter
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Applied Manifold Geometry 433M, we
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Applied Manifold Geometry 435The cu
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Applied Manifold Geometry 437(iv) (
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Applied Manifold Geometry 439where
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. ..Applied Manifold Geometry 441in
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Applied Manifold Geometry 443⌋ is
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Applied Manifold Geometry 445Now, a
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Applied Manifold Geometry 447symmet
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Applied Manifold Geometry 449study
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Applied Manifold Geometry 451togeth
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Applied Manifold Geometry 453result
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Applied Manifold Geometry 455will b
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Applied Manifold Geometry 457g 11 =
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Applied Manifold Geometry 459is def
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Applied Manifold Geometry 461ordere
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Applied Manifold Geometry 463Now, r
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Applied Manifold Geometry 465Simila
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Applied Manifold Geometry 467which
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Applied Manifold Geometry 469From t
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Applied Manifold Geometry 471where
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Applied Manifold Geometry 4733.17.2
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Applied Manifold Geometry 475On the
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Applied Manifold Geometry 477ing di
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Applied Manifold Geometry 479Note t
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Applied Manifold Geometry 481Then w
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Applied Manifold Geometry 483consis
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Chapter 4Applied Bundle Geometry4.1
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Applied Bundle Geometry 487is calle
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Applied Bundle Geometry 489V and an
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Applied Bundle Geometry 4914.3 Vect
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Applied Bundle Geometry 493dimensio
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Applied Bundle Geometry 495orthogon
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Applied Bundle Geometry 497t, is a
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Applied Bundle Geometry 499Let T Y
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Applied Bundle Geometry 501In other
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Applied Bundle Geometry 503we shall
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Applied Bundle Geometry 505Pendulum
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Applied Bundle Geometry 507Using L
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Applied Bundle Geometry 509the isom
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Applied Bundle Geometry 511theory f
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Applied Bundle Geometry 513of the c
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Applied Bundle Geometry 515where Ω
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Applied Bundle Geometry 517nals, th
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Applied Bundle Geometry 519(1985)])
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Applied Bundle Geometry 521finite-d
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Applied Bundle Geometry 523and thes
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Applied Bundle Geometry 525Now, let
- Page 562 and 563:
Applied Bundle Geometry 527gravity
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Applied Bundle Geometry 529a Dp−b
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Applied Bundle Geometry 531A princi
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Applied Bundle Geometry 533is the r
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Applied Bundle Geometry 535Now, let
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Applied Bundle Geometry 537By cycli
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Applied Bundle Geometry 5394.9.2 Fe
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Applied Bundle Geometry 541This lin
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Applied Bundle Geometry 543(1) L g
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Applied Bundle Geometry 545and ω 0
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Applied Bundle Geometry 547isfiesω
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Applied Bundle Geometry 549of the c
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Applied Bundle Geometry 551Controll
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Applied Bundle Geometry 553Foliatio
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Applied Bundle Geometry 555ψ : (x,
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Applied Bundle Geometry 557from res
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Applied Bundle Geometry 559Motion a
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Applied Bundle Geometry 561where Z
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Applied Bundle Geometry 563Systems
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Applied Bundle Geometry 5653. Recal
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Applied Bundle Geometry 567Therefor
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Applied Bundle Geometry 569smooth m
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Applied Bundle Geometry 571state va
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Applied Bundle Geometry 573The geom
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Applied Bundle Geometry 575Y ∋ y
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Applied Bundle Geometry 577autonomo
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Applied Bundle Geometry 579(see 3.1
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Applied Bundle Geometry 581and init
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Applied Bundle Geometry 583potentia
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Applied Bundle Geometry 585effector
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Applied Bundle Geometry 587Fig. 4.9
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Applied Bundle Geometry 589physical
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Applied Bundle Geometry 591open Lio
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Applied Bundle Geometry 593et al. (
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Applied Bundle Geometry 595(2) Acti
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Applied Bundle Geometry 597˙Φ ≤
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Applied Bundle Geometry 599number o
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Applied Bundle Geometry 601where Ψ
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Applied Bundle Geometry 603ing to c
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Applied Bundle Geometry 605where [
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Applied Bundle Geometry 607interval
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Applied Bundle Geometry 609The foll
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Applied Bundle Geometry 611In parti
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Applied Bundle Geometry 613The pull
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Applied Bundle Geometry 615(2) δ
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Applied Bundle Geometry 617of unita
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Applied Bundle Geometry 619system o
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Applied Bundle Geometry 621of H pre
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Applied Bundle Geometry 623It follo
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Applied Bundle Geometry 625a produc
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Applied Bundle Geometry 627B Ham(M)
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Applied Bundle Geometry 629b.Let us
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Applied Bundle Geometry 631If P is
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Applied Bundle Geometry 633question
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Applied Bundle Geometry 635spheres
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Applied Bundle Geometry 637be thoug
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Applied Bundle Geometry 639of the b
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Applied Bundle Geometry 641in C 1 (
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Applied Bundle Geometry 643from a t
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Applied Bundle Geometry 645Now let
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Applied Bundle Geometry 647for t <
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Applied Bundle Geometry 649is a Ham
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Applied Bundle Geometry 651The foll
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Applied Bundle Geometry 653is the u
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Applied Bundle Geometry 655every no
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Applied Bundle Geometry 657P × P w
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Applied Bundle Geometry 659that the
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Applied Bundle Geometry 661extend t
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Applied Bundle Geometry 663identity
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Applied Bundle Geometry 665The mapw
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Applied Bundle Geometry 667It is a
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Applied Bundle Geometry 669I Q is i
- Page 706 and 707:
Applied Bundle Geometry 671whereC i
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Applied Bundle Geometry 673form Q.
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Applied Bundle Geometry 675τ( exp(
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Applied Bundle Geometry 6774.13.2.2
- Page 714 and 715:
Applied Bundle Geometry 679Therefor
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Applied Bundle Geometry 6814.13.2.3
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Applied Bundle Geometry 683⎛⎞co
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Applied Bundle Geometry 685Usually,
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Applied Bundle Geometry 687on the s
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Applied Bundle Geometry 6894.13.2.5
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Applied Bundle Geometry 6914.13.3 P
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Applied Bundle Geometry 693Since T
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Applied Bundle Geometry 695On the o
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Applied Bundle Geometry 697may writ
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Applied Bundle Geometry 699determin
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Applied Bundle Geometry 701section,
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Applied Bundle Geometry 703for deri
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Applied Bundle Geometry 705dictions
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Applied Bundle Geometry 707too sing
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Applied Bundle Geometry 709In (4.18
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Applied Bundle Geometry 7114.13.4.4
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Applied Bundle Geometry 713sis repr
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Applied Bundle Geometry 7154.13.4.6
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Applied Bundle Geometry 717a (linea
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Applied Bundle Geometry 719past few
- Page 756 and 757:
Applied Bundle Geometry 721global q
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Applied Bundle Geometry 7239. It ha
- Page 760 and 761:
Applied Bundle Geometry 725needs to
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Applied Bundle Geometry 727pear at
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Applied Bundle Geometry 729X, F A i
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Applied Bundle Geometry 731ifolds,
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Applied Bundle Geometry 733and not
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Applied Bundle Geometry 735under U(
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Applied Bundle Geometry 737N = 2 br
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Applied Bundle Geometry 739thusa
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Applied Bundle Geometry 741antisymm
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Applied Bundle Geometry 743see this
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Applied Bundle Geometry 745Coupling
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Applied Bundle Geometry 747acts as
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Applied Bundle Geometry 749good coo
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Applied Bundle Geometry 751Φ. Brea
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Applied Bundle Geometry 753equating
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Applied Bundle Geometry 755differen
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Applied Bundle Geometry 7574.14.10
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Applied Bundle Geometry 759deformed
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Applied Bundle Geometry 761phenomen
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Applied Bundle Geometry 763appears
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Applied Bundle Geometry 7654.14.10.
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Applied Bundle Geometry 767For J >
- Page 804 and 805:
Applied Bundle Geometry 769K 1/2
- Page 806 and 807:
Applied Bundle Geometry 771(i) The
- Page 808 and 809:
Applied Bundle Geometry 773by α =
- Page 810 and 811:
Applied Bundle Geometry 775(4.279)
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Applied Bundle Geometry 777Λ ⊗
- Page 814 and 815:
Applied Bundle Geometry 779coupling
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Applied Bundle Geometry 781where we
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Applied Bundle Geometry 783The posi
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Applied Bundle Geometry 785Although
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Applied Bundle Geometry 787Let us a
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Applied Bundle Geometry 789of the t
- Page 826 and 827:
Applied Bundle Geometry 791The Riem
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Applied Bundle Geometry 793To compl
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Applied Bundle Geometry 795Ω 1 :Ω
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Chapter 5Applied Jet GeometryModern
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Applied Jet Geometry 799x, with coe
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Applied Jet Geometry 801s i (x), as
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Applied Jet Geometry 803It is conve
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Applied Jet Geometry 805has the 1
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Applied Jet Geometry 807which split
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Applied Jet Geometry 809gives the h
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Applied Jet Geometry 811Furthermore
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Applied Jet Geometry 813This is a c
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Applied Jet Geometry 815Due to this
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Applied Jet Geometry 817The affine
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Applied Jet Geometry 819In particul
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Applied Jet Geometry 821Building on
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Applied Jet Geometry 823on J ∞ (X
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Applied Jet Geometry 825its tangent
- Page 862 and 863:
Applied Jet Geometry 827Fig. 5.3 Hi
- Page 864 and 865:
Applied Jet Geometry 829It follows
- Page 866 and 867:
Applied Jet Geometry 831affine, whi
- Page 868 and 869:
Applied Jet Geometry 833where Γ i
- Page 870 and 871:
Applied Jet Geometry 8355.6.5 Jacob
- Page 872 and 873:
Applied Jet Geometry 837is also the
- Page 874 and 875:
Applied Jet Geometry 839A generic m
- Page 876 and 877:
Applied Jet Geometry 841where ϑ eH
- Page 878 and 879:
Applied Jet Geometry 843Since E L|
- Page 880 and 881:
Applied Jet Geometry 845Thus, every
- Page 882 and 883:
Applied Jet Geometry 847along u. Ev
- Page 884 and 885:
Applied Jet Geometry 849equations c
- Page 886 and 887:
Applied Jet Geometry 851A Hamiltoni
- Page 888 and 889:
Applied Jet Geometry 853Connections
- Page 890 and 891:
Applied Jet Geometry 855Lagrangian
- Page 892 and 893:
Applied Jet Geometry 857on V ∗ M.
- Page 894 and 895:
Applied Jet Geometry 859contain no
- Page 896 and 897:
Applied Jet Geometry 861(ii) For an
- Page 898 and 899:
Applied Jet Geometry 8635.6.16 Lyap
- Page 900 and 901:
Applied Jet Geometry 865for any t >
- Page 902 and 903:
Applied Jet Geometry 867vertical co
- Page 904 and 905:
Applied Jet Geometry 869difficulty,
- Page 906 and 907:
Applied Jet Geometry 871the energy
- Page 908 and 909:
Applied Jet Geometry 873by the tran
- Page 910 and 911:
Applied Jet Geometry 875The conditi
- Page 912 and 913:
Applied Jet Geometry 877Let Γ = (M
- Page 914 and 915:
Applied Jet Geometry 879geometrical
- Page 916 and 917:
Applied Jet Geometry 881Let (M, I)
- Page 918 and 919:
Applied Jet Geometry 883so referrin
- Page 920 and 921:
Applied Jet Geometry 885The Poincar
- Page 922 and 923:
Applied Jet Geometry 887where N n
- Page 924 and 925:
Applied Jet Geometry 889be a projec
- Page 926 and 927:
Applied Jet Geometry 891to differen
- Page 928 and 929:
Applied Jet Geometry 893for every c
- Page 930 and 931:
Applied Jet Geometry 895vector-fiel
- Page 932 and 933:
Applied Jet Geometry 897This is phr
- Page 934 and 935:
Applied Jet Geometry 899where a, b
- Page 936 and 937:
Applied Jet Geometry 901represent t
- Page 938 and 939:
Applied Jet Geometry 903̂L : J 1 (
- Page 940 and 941:
Applied Jet Geometry 905space J 1 (
- Page 942 and 943:
Applied Jet Geometry 907First of al
- Page 944 and 945:
Applied Jet Geometry 909Therefore,
- Page 946 and 947:
Applied Jet Geometry 911Recall that
- Page 948 and 949:
Applied Jet Geometry 9135.11 Applic
- Page 950 and 951:
Applied Jet Geometry 915the vector
- Page 952 and 953:
Applied Jet Geometry 9175.11.4 Gaug
- Page 954 and 955:
Applied Jet Geometry 9195.11.5 Lagr
- Page 956 and 957:
Applied Jet Geometry 921are represe
- Page 958 and 959:
Applied Jet Geometry 923which are t
- Page 960 and 961:
Applied Jet Geometry 925of this fun
- Page 962 and 963:
Applied Jet Geometry 927a principal
- Page 964 and 965:
Applied Jet Geometry 929Recall that
- Page 966 and 967:
Applied Jet Geometry 931Moreover, t
- Page 968 and 969:
Applied Jet Geometry 933other only
- Page 970 and 971:
Applied Jet Geometry 935In particul
- Page 972 and 973:
Applied Jet Geometry 937Note that,
- Page 974 and 975:
Applied Jet Geometry 939This equali
- Page 976 and 977:
Applied Jet Geometry 941Then, the s
- Page 978 and 979:
Applied Jet Geometry 943In the Lagr
- Page 980 and 981:
Applied Jet Geometry 945Let τ be a
- Page 982 and 983:
Applied Jet Geometry 947Using (5.42
- Page 984 and 985:
Applied Jet Geometry 949associated
- Page 986 and 987:
Applied Jet Geometry 951parts,F α
- Page 988 and 989:
Applied Jet Geometry 953of the Hilb
- Page 990 and 991:
Applied Jet Geometry 955For example
- Page 992 and 993:
Applied Jet Geometry 957the convent
- Page 994 and 995:
Applied Jet Geometry 959left ideal
- Page 996 and 997:
Applied Jet Geometry 961LX → Σ i
- Page 998 and 999:
Applied Jet Geometry 963Levi-Civita
- Page 1000 and 1001:
Applied Jet Geometry 965see this fr
- Page 1002 and 1003:
Applied Jet Geometry 967curves. And
- Page 1004 and 1005:
Applied Jet Geometry 969One sees th
- Page 1006 and 1007:
Applied Jet Geometry 971sums over a
- Page 1008 and 1009:
Applied Jet Geometry 973all this to
- Page 1010 and 1011:
Applied Jet Geometry 975universe ev
- Page 1012 and 1013:
Applied Jet Geometry 977on Σ. If M
- Page 1014 and 1015:
Applied Jet Geometry 979(1) Lorentz
- Page 1016 and 1017:
Applied Jet Geometry 981terpret thi
- Page 1018 and 1019:
Chapter 6Geometrical Path Integrals
- Page 1020 and 1021:
Geometrical Path Integrals and Thei
- Page 1022 and 1023:
Geometrical Path Integrals and Thei
- Page 1024 and 1025:
Geometrical Path Integrals and Thei
- Page 1026 and 1027:
Geometrical Path Integrals and Thei
- Page 1028 and 1029:
Geometrical Path Integrals and Thei
- Page 1030 and 1031:
Geometrical Path Integrals and Thei
- Page 1032 and 1033:
Geometrical Path Integrals and Thei
- Page 1034 and 1035:
Geometrical Path Integrals and Thei
- Page 1036 and 1037:
Geometrical Path Integrals and Thei
- Page 1038 and 1039:
Geometrical Path Integrals and Thei
- Page 1040 and 1041:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1044 and 1045:
Geometrical Path Integrals and Thei
- Page 1046 and 1047:
Geometrical Path Integrals and Thei
- Page 1048 and 1049:
Geometrical Path Integrals and Thei
- Page 1050 and 1051:
Geometrical Path Integrals and Thei
- Page 1052 and 1053:
Geometrical Path Integrals and Thei
- Page 1054 and 1055:
Geometrical Path Integrals and Thei
- Page 1056 and 1057:
Geometrical Path Integrals and Thei
- Page 1058 and 1059:
Geometrical Path Integrals and Thei
- Page 1060 and 1061:
Geometrical Path Integrals and Thei
- Page 1062 and 1063:
Geometrical Path Integrals and Thei
- Page 1064 and 1065:
Geometrical Path Integrals and Thei
- Page 1066 and 1067:
Geometrical Path Integrals and Thei
- Page 1068 and 1069:
Geometrical Path Integrals and Thei
- Page 1070 and 1071:
Geometrical Path Integrals and Thei
- Page 1072 and 1073:
Geometrical Path Integrals and Thei
- Page 1074 and 1075:
Geometrical Path Integrals and Thei
- Page 1076 and 1077:
Geometrical Path Integrals and Thei
- Page 1078 and 1079:
Geometrical Path Integrals and Thei
- Page 1080 and 1081:
Geometrical Path Integrals and Thei
- Page 1082 and 1083:
Geometrical Path Integrals and Thei
- Page 1084 and 1085:
Geometrical Path Integrals and Thei
- Page 1086 and 1087:
Geometrical Path Integrals and Thei
- Page 1088 and 1089:
Geometrical Path Integrals and Thei
- Page 1090 and 1091:
Geometrical Path Integrals and Thei
- Page 1092 and 1093:
Geometrical Path Integrals and Thei
- Page 1094 and 1095:
Geometrical Path Integrals and Thei
- Page 1096 and 1097:
Geometrical Path Integrals and Thei
- Page 1098 and 1099:
Geometrical Path Integrals and Thei
- Page 1100 and 1101:
Geometrical Path Integrals and Thei
- Page 1102 and 1103:
Geometrical Path Integrals and Thei
- Page 1104 and 1105:
Geometrical Path Integrals and Thei
- Page 1106 and 1107:
Geometrical Path Integrals and Thei
- Page 1108 and 1109:
Geometrical Path Integrals and Thei
- Page 1110 and 1111:
Geometrical Path Integrals and Thei
- Page 1112 and 1113:
Geometrical Path Integrals and Thei
- Page 1114 and 1115:
Geometrical Path Integrals and Thei
- Page 1116 and 1117:
Geometrical Path Integrals and Thei
- Page 1118 and 1119:
Geometrical Path Integrals and Thei
- Page 1120 and 1121:
Geometrical Path Integrals and Thei
- Page 1122 and 1123:
Geometrical Path Integrals and Thei
- Page 1124 and 1125:
Geometrical Path Integrals and Thei
- Page 1126 and 1127:
Geometrical Path Integrals and Thei
- Page 1128 and 1129:
Geometrical Path Integrals and Thei
- Page 1130 and 1131:
Geometrical Path Integrals and Thei
- Page 1132 and 1133:
Geometrical Path Integrals and Thei
- Page 1134 and 1135:
Geometrical Path Integrals and Thei
- Page 1136 and 1137:
Geometrical Path Integrals and Thei
- Page 1138 and 1139:
Geometrical Path Integrals and Thei
- Page 1140 and 1141:
Geometrical Path Integrals and Thei
- Page 1142 and 1143:
Geometrical Path Integrals and Thei
- Page 1144 and 1145:
Geometrical Path Integrals and Thei
- Page 1146 and 1147:
Geometrical Path Integrals and Thei
- Page 1148 and 1149:
Geometrical Path Integrals and Thei
- Page 1150 and 1151:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1154 and 1155:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1174 and 1175:
Geometrical Path Integrals and Thei
- Page 1176 and 1177:
Geometrical Path Integrals and Thei
- Page 1178 and 1179:
Geometrical Path Integrals and Thei
- Page 1180 and 1181:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1188 and 1189:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1198 and 1199:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1202 and 1203:
Geometrical Path Integrals and Thei
- Page 1204 and 1205:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1210 and 1211:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1214 and 1215:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1222 and 1223:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1226 and 1227:
Geometrical Path Integrals and Thei
- Page 1228 and 1229:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1254 and 1255:
Geometrical Path Integrals and Thei
- Page 1256 and 1257:
Geometrical Path Integrals and Thei
- Page 1258 and 1259:
Geometrical Path Integrals and Thei
- Page 1260 and 1261:
Geometrical Path Integrals and Thei
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Geometrical Path Integrals and Thei
- Page 1264 and 1265:
Geometrical Path Integrals and Thei
- Page 1266 and 1267:
Geometrical Path Integrals and Thei
- Page 1268 and 1269:
Geometrical Path Integrals and Thei
- Page 1270 and 1271:
Geometrical Path Integrals and Thei
- Page 1272 and 1273:
Geometrical Path Integrals and Thei
- Page 1274 and 1275:
Geometrical Path Integrals and Thei
- Page 1276 and 1277:
Geometrical Path Integrals and Thei
- Page 1278 and 1279:
Geometrical Path Integrals and Thei
- Page 1280 and 1281:
Geometrical Path Integrals and Thei
- Page 1282 and 1283:
Geometrical Path Integrals and Thei
- Page 1284 and 1285:
Geometrical Path Integrals and Thei
- Page 1286 and 1287:
Geometrical Path Integrals and Thei
- Page 1288 and 1289:
BibliographyAblowitz, M.J., Clarkso
- Page 1290 and 1291:
Bibliography 1255equations. Springe
- Page 1292 and 1293:
Bibliography 1257connections, Phys.
- Page 1294 and 1295:
Bibliography 1259JHEP 0003:007.Bran
- Page 1296 and 1297: Bibliography 1261Clementi, C. Petti
- Page 1298 and 1299: Bibliography 1263Domany, E., Van He
- Page 1300 and 1301: Bibliography 1265geometrical signat
- Page 1302 and 1303: Bibliography 1267Bergmann theory of
- Page 1304 and 1305: Bibliography 1269to Complex Systems
- Page 1306 and 1307: Bibliography 1271Action for String
- Page 1308 and 1309: Bibliography 1273Ivancevic, V., Bea
- Page 1310 and 1311: Bibliography 1275Krener, A. (1984).
- Page 1312 and 1313: Bibliography 1277Li, M., Vitanyi, P
- Page 1314 and 1315: Bibliography 1279Nature, 261(5560),
- Page 1316 and 1317: Bibliography 1281Lambert and R. Gol
- Page 1318 and 1319: Bibliography 1283dynamics of human
- Page 1320 and 1321: Bibliography 1285Reshetikhin, N.Yu,
- Page 1322 and 1323: Bibliography 1287Rev. E, 58, 6333-6
- Page 1324 and 1325: Bibliography 1289Stasheff, J.D. (19
- Page 1326 and 1327: Bibliography 1291matical Physics. S
- Page 1328 and 1329: Bibliography 1293Witten, E. (1991).
- Page 1330 and 1331: Index1−jet bundle, 8271−jet lif
- Page 1332 and 1333: Index 1297Chan-Paton factor, 1238Ch
- Page 1334 and 1335: Index 1299Dirac-Born-Infeld theory,
- Page 1336 and 1337: Index 1301Gauss, 5Gauss map, 284Gau
- Page 1338 and 1339: Index 1303isometric, 17isomorphic,
- Page 1340 and 1341: Index 1305Maxwell Lagrangian, 34Max
- Page 1342 and 1343: Index 1307probability manifold, 333
- Page 1344 and 1345: Index 1309super-space, 1215supercov
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