Constructions of harmonic maps between Hadamard manifolds

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$Tohoku Math. J. First Series General Index$

BIBLIOGRAPHY 85 [21] A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc. 258 (1980), 147–153. [22] A. Kasue and T. Washio, Growth of equivariant harmonic maps and harmonic morphisms, Osaka J. Math. 27 (1990), 899–928. [23] M. Lanzendorf, Einstein metrics with nonpositive sectional curvature on extensions of Lie algebras of Heisenberg type, Geom. Dedicata 66 (1997), 187–202. [24] S.Y. Li and L. Ni, On the holomorphicity of proper harmonic maps between unit balls with the Bergman metrics, Math. Ann. 316 (2000), 333–354. [25] P. Li and L.-F. Tam, The heat equation and harmonic maps of complete manifolds, Invent. Math. 105 (1991), 1–46. [26] P. Li and L.-F. Tam, Uniqueness and regularity of proper harmonic maps, Ann. of Math. 137 (1993), 167–201. [27] P. Li and L.-F. Tam, Uniqueness and regularity of proper harmonic maps II, Indiana Univ. Math. J. 42 (1993), 591–635. [28] T. Nagasawa and A. Tachikawa, Blow-up solutions for ordinary differential equations associated to harmonic maps and their applications, J. Math. Soc. Japan 53 (2001), 485–500. [29] T. Nagasawa and K. Ueno, Initial-final value problems for ordinary differential equations and applications to equivariant harmonic maps, J. Math. Soc. Japan 50 (1998), 545–555. [30] M. Parker, Orthogonal multiplications in small dimensions, Bull. London Math. Soc. 15 (1983), 368–372. [31] A. Ratto, Harmonic maps of spheres and the Hopf construction, Topology 28 (1989), 379–388.
86 BIBLIOGRAPHY [32] A. Ratto and M. Rigoli, On the asymptotic behaviour of rotationally symmetric harmonic maps, J. Differential Equations 101 (1993), 15–27. [33] R. Schoen and S. T. Yau Compact group actions and the topology of the manifolds with nonpositive curvature, Topology 18 (1979), 361–380. [34] R. T. Smith, Harmonic mappings of spheres, Amer. J. Math. 97 (1975), 364–385. [35] A. Tachikawa, A nonexistence result for harmonic mappings from R n into H n , Tokyo J. Math. 11 (1988), 311–316. [36] A. Tachikawa, Harmonic mappings from R m into a Hadamard manifold, J. Math. Soc. Japan 42 (1990), 147–153. [37] G. Toth, Classification of quadratic harmonic maps of S 3 into spheres, Indiana Univ. Math. J. 36 (1987), 231–239 [38] K. Ueno, Some new examples of eigenmaps from S m into S n , Proc. Japan Acad. 69 (1993), 205–208. [39] K. Ueno, A study of ordinary differential equations arising from equivariant harmonic maps, Tokyo J. Math. 17 (1994), 395–416. [40] K. Ueno, The Dirichlet problem for harmonic maps between Damek-Ricci spaces, Tôhoku Math. J. 49 (1997), 565–575. [41] K. Ueno, Non-existence of proper harmonic maps from complex hyperbolic spaces into real hyperbolic spaces, preprint. [42] H. Urakawa, Equivariant harmonic maps between compact Riemannian manifolds of cohomogeneity one, Michigan Math. J. 40 (1993), 27–51. [43] H. Urakawa and K. Ueno, Equivariant harmonic maps associated to large group actions, Tokyo J. Math. 17 (1994), 417–437.
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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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1.2. GLOBAL PROPERTIES OF SOLUTIONS
Page 38 and 39: 1.2. GLOBAL PROPERTIES OF SOLUTIONS
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 86 and 87: Bibliography [1] K. Akutagawa, Harm
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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