Blaga P. Lectures on the differential geometry of - tiera.ru

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To Cristina, with love
Page 1: Lectures on the Di
Page 6 and 7: 6 Contents 1.10.1 The geometrical m
Page 8 and 9: 8 Contents 5.1.3 Envelope of a fami
Page 10 and 11: 10 Foreword The material included i
Page 13 and 14: 1.1 Introduction CHAPTER 1 Space cu
Page 15 and 16: 1.2. Parameterized curves (paths) 1
Page 17 and 18: 1.2. Parameterized curves (paths) 1
Page 19 and 20: though, as mentioned, they have the
Page 21 and 22: and, hence, 1.2. Parameterized curv
Page 23 and 24: 1.3. The definition of the curve 23
Page 25 and 26: 1.3. The definition of the curve 25
Page 27 and 28: 1.4. Analytical representations of
Page 33 and 34: 1.5. The tangent and the normal pla
Page 35 and 36: 1.5. The tangent and the normal pla
Page 37 and 38: or, in a more familiar form, while
Page 39 and 40: Thus, from the equation of the tang
Page 41 and 42: Thus, lim ∆t→0 d(∆t) = lim |
Page 43 and 44: 1.7. The curvature of a curve 43 Su
Page 45 and 46: 1.8. The Frenet frame 45 system wit
Page 47 and 48: Then, having in mind that and we ge
Page 49 and 50: 1.9. Oriented curves. The Frenet fr
Page 51 and 52: therefore, 1.10. The Frenet formula
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1.10. The Frenet formulae. The tors
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1.11. The local behaviour of a para
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1.12. The contact between a space c
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1.13. The contact between a space c
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1.14. Existence and uniqueness theo
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2.1 Introduction CHAPTER 2 Plane cu
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2.2. Envelopes of plane curves 77 C
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2.2. Envelopes of plane curves 79 2
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2.3. The curvature of a plane curve
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2.4. The curvature center. The evol
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2.4. The curvature center. The evol
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2.5. The osculating circle of a cur
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2.6. The existence and uniqueness t
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CHAPTER 3 The integration of the na
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3.2. Examples for the integration o
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Problems 1. Write the equations of
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Problems 105 14. A circular disk of
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26. Show that all the normals to th
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Problems 109 45. Let M be an arbitr
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Problems 111 57. Consider the curve
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Part II Surfaces
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116 Chapter 4. General theory of su
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186 Chapter 5. Special classes of s
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218 Problems 4. Find the equations
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220 Problems 23. Find the tangent p
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222 Problems 5. x2 p 6. x2 p + y2 q
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224 Problems from the right helicoi
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226 Problems 62. Show that at each
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228 Problems
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230 Bibliography [11] Dupin, Ch. -
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232 Bibliography [45] Osserman, R.
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234 Index 200, 213, 214 geodesic, 1
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236 Index of a curve, 48, 49 of a s
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Blaga P. Lectures on the differential geometry of - tiera.ru

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