Constructions of harmonic maps between Hadamard manifolds

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Bibliography [1] K. Akutagawa, Harmonic diffeomorphisms of the hyperbolic plane, Trans. Amer. Math. Soc. 342 (1994), 325–342. [2] K. Akutagawa and T. Tachikawa, Nonexistence results for harmonic maps between noncompact complete Riemannian manifolds, Tokyo J. Math. 16 (1993), 131–145. [3] P. Baird, Harmonic maps with symmetry, harmonic morphisms and deformations of metrics, Research Notes in Math. 87, Pitman, Boston, MA, 1983. [4] J. Boggino, Generalized Heisenberg groups and solvmanifolds naturally associated, Rend. Sem. Mat. Univ. Politec. Torino 43 (1985), 529–547. [5] J. Berndt, F. Tricerri and L. Vanhecke, Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lecture Notes in Math. 1598, Springer-Verlag, Berlin, Heidelberg, New York, 1995. [6] M. Cowling, A. H. Dooley, A. Korányi and F. Ricci, H-type groups and Iwasawa decompositions, Adv. Math. 87 (1991), 1–41. [7] E. Damek, Curvature of a semi-direct extension of a Heisenberg type nilpotent group, Colloq. Math. 53 (1987), 249–253. [8] E. Damek, The geometry of a semi-direct extension of a Heisenberg type nilpotent group, Colloq. Math. 53 (1987), 255–268. 83
84 BIBLIOGRAPHY [9] E. Damek and F. Ricci, A class of nonsymmetric harmonic Riemannian spaces, Bull. Amer. Math. Soc. 27 (1992), 139–142. [10] E. Damek and F. Ricci, Harmonic analysis on solvable extensions of H-type groups, J. Geom. Anal. 2 (1992), 213–248. [11] W. Y. Ding, Symmetric harmonic maps between spheres, Comm. Math. Phys. 118 (1988), 641–649. [12] H. Donnelly, Dirichlet problem at infinity for harmonic maps: rank one symmetric spaces, Trans. Amer. Math. Soc. 344 (1994), 713–735. [13] I. Dotti, On the curvature of certain extensions of H-type groups, Proc. Amer. Math. Soc. 125 (1997), 573–578. [14] P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. [15] J. Eells and A. Ratto, Harmonic maps between spheres and ellipsoids, Internat. J. Math. 1 (1990), 1–27. [16] J. Eells and A. Ratto, Harmonic maps and minimal immersions with symmetries, Ann. of Math. Stud. 130, Princeton University Press, Princeton, NJ, 1993. [17] J. Eells and H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. [18] H. Gauchman and G. Toth, Constructions of harmonic polynomial maps between spheres, Geom. Dedicata 50 (1994), 57–79. [19] R. S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Math. 471, Springer-Verlag, Berlin-New York, 1975. [20] P. Hartman, On homotopic harmonic mappings, Canad. J. Math. 19 (1967), 673–687.
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ISSN 1343-9499 TOHOKU MATHEMATICAL
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Constructions of harmonic maps betw
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2 Abstract In this thesis, we prese
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4 Introduction Let (M,g) and (M ′
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6 that for any point z ∈ S m+n−
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8 Equivariant harmonic maps have be
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10 vanishing sectional curvatures f
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CHAPTER 1 Ordinary differential equ
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1.1. LOCAL EXISTENCE OF SOLUTIONS T
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1.2. GLOBAL PROPERTIES OF SOLUTIONS
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Page 44 and 45: 1.3. ADDENDUM 41 Theorem 1.2.11. Th
Page 46 and 47: CHAPTER 2 Equivariant harmonic maps
Page 48 and 49: 2.1. EIGENMAPS 45 Following a metho
Page 50 and 51: 2.1. EIGENMAPS 47 Then the restrict
Page 52 and 53: 2.1. EIGENMAPS 49 exists a full ort
Page 54 and 55: 2.2. REDUCTION OF HARMONIC MAP EQUA
Page 56 and 57: 2.3. CONSTRUCTIONS OF EQUIVARIANT H
Page 58 and 59: 2.3. CONSTRUCTIONS OF EQUIVARIANT H
Page 60: 2.3. CONSTRUCTIONS OF EQUIVARIANT H
Page 63 and 64: 60 CHAPTER 3. DAMEK-RICCI SPACES a
Page 65 and 66: 62 CHAPTER 3. DAMEK-RICCI SPACES in
Page 67 and 68: 64 CHAPTER 3. DAMEK-RICCI SPACES wh
Page 69 and 70: 66 CHAPTER 3. DAMEK-RICCI SPACES (2
Page 71 and 72: 68 CHAPTER 3. DAMEK-RICCI SPACES Si
Page 73 and 74: 70 CHAPTER 3. DAMEK-RICCI SPACES Th
Page 76 and 77: CHAPTER 4 Non-existence of proper h
Page 78 and 79: 4.1. PROOF OF THEOREM 75 Moreover,
Page 80 and 81: 4.1. PROOF OF THEOREM 77 Propositio
Page 82 and 83: 4.2. A COUNTER EXAMPLE 79 where (y,
Page 84 and 85: 4.2. A COUNTER EXAMPLE 81 Hence we
Page 88 and 89: BIBLIOGRAPHY 85 [21] A. Kaplan, Fun
Page 90 and 91: BIBLIOGRAPHY 87 [44] R. Wood, Polyn
Page 92: No.16 Tatsuo Konno: On the infinite
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Constructions of harmonic maps between Hadamard manifolds

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