Differential Geometry: Proceedings of the VIII International Colloquium

CONTENTS......Page 10
Preface......Page 6
Organizing Committees......Page 8
A brief portrait of the life and work of Professor Enrique Vidal Abascal L. A. Cordero......Page 14
Part A Foliation theory......Page 22
1. Introduction......Page 24
2. Classifying spaces......Page 26
3. Primary classes......Page 29
4. Secondary classes......Page 34
5. Variation of secondary classes......Page 40
6. Molino Structure Theory......Page 43
7. Some open problems......Page 45
References......Page 46
1. Introduction......Page 49
2. The construction......Page 51
3. Questions......Page 54
References......Page 55
1. Introduction......Page 56
2. Uniform perfectness of diffeomorphism groups......Page 59
3. Uniform simplicity of the diffeomorphism groups......Page 64
References......Page 68
1. Thurston's Inequality......Page 69
2. Thurston's Absolute Inequality for Spinnable Foliations......Page 72
3. Dehn Filling......Page 73
4. Bennequin's Isotopy Lemma......Page 74
References......Page 76
1. Introduction......Page 78
2. Definition of the Fatou and Julia sets......Page 79
3. Some properties of Julia sets......Page 83
4. Examples......Page 84
References......Page 86
1. Introduction......Page 88
2. Preliminaries......Page 90
3. Geometric arguments......Page 92
4. Topological arguments......Page 93
References......Page 94
0. Introduction......Page 96
1. Main Results......Page 98
2.1. Algebraic preliminaries......Page 100
2.3. Variational formulae......Page 102
References......Page 106
1. Introduction......Page 107
2. Canonical differential operators defined on a Riemannian foliation......Page 108
3. Adiabatic limits and Riemannian foliations......Page 110
4. A transversal Weitzenböck formula......Page 112
References......Page 114
1. The duality......Page 115
References......Page 116
Open problems on foliations......Page 117
Part B Riemannian geometry......Page 122
1. Introduction......Page 124
2. Killing graphs......Page 125
3. Riemannian submersions......Page 126
4. Conformal Killing graphs......Page 128
References......Page 132
1. Introduction......Page 133
2.1. Local theory for the isometric case......Page 134
2.3. Digression: Extending intrinsic isometries......Page 135
3. Higher codimensions: Rigidity results......Page 136
3.1. The s-nullity and the conformal s-nullity......Page 137
3.2. A main tool: flat bilinear forms......Page 138
3.3. Conformal geometry in the light cone......Page 139
4. The general deformation problem......Page 140
5. Genuine deformations......Page 141
5.2. Genuine conformal deformations of submanifolds......Page 143
5.3. Constructing conformal pairs from isometric ones......Page 145
References......Page 147
1. Totally geodesic submanifolds......Page 149
2. Maximal totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2......Page 151
2.1. G +2 (Rn+2)......Page 152
2.2. G2 (Cn+2)......Page 154
2.3. G (Hn+2)......Page 155
2.7. E6=(U(1) Spin(10))......Page 156
2.12. G2......Page 157
References......Page 158
The orbits of cohomogeneity one actions on complex hyperbolic spaces J. C. Díaz-Ramos......Page 159
1. The geometry of the orbits......Page 160
2. Hypersurfaces with constant principal curvatures......Page 167
References......Page 168
1. Introduction......Page 169
2. Preliminaries......Page 170
3. Proof of Theorem 1.1......Page 172
4. Rigidity results in the Euclidean space......Page 175
References......Page 176
1. Introduction......Page 177
2. Bernstein-Calabi and Heinz-Chern type results......Page 179
3. The mean curvature flow......Page 181
4. Homotopy to a constant map......Page 185
Acknowledgements......Page 186
References......Page 187
1. Introduction......Page 188
1.2. Osserman geometry......Page 189
1.3. Affine geometry......Page 190
1.4. Torsion free connections and Riemannian geometry......Page 191
2. The proof of Theorem 1.3......Page 192
References......Page 197
1. Introduction......Page 198
2. Preliminaries......Page 199
3. Conformally Osserman multiply warped products......Page 200
4. Locally conformally at multiply warped products......Page 201
6. Multiply warped products of constant curvature......Page 204
References......Page 207
1. Riemannian reductive homogeneous spaces......Page 208
2.1. -symmetric spaces......Page 209
2.3. Riemannian and Indefinite Riemannian -symmetric spaces......Page 210
2.4. Irreducible Riemannian -symmetric spaces......Page 211
3. Classification of compact simple Z2 symmetric spaces......Page 213
4.1. Z2 -symmetric metrics on flag manifolds......Page 214
4.2. The Z2 -Riemannian symmetric space SO(2m)=Sp(m)......Page 216
References......Page 219
1. Introduction and preliminaries......Page 220
2. Preliminaries about H-type groups......Page 222
3.1. Constant osculating rank of the Jacobi operator along a special family of geodesics......Page 223
3.2. Resolution of the Jacobi equation......Page 225
3.3. Relation between both methods......Page 227
References......Page 229
1. Introduction......Page 230
2. Homogeneous geodesics in pseudo-Riemannian manifolds......Page 231
3. Homogeneous geodesics in affine manifolds......Page 232
5. G.o. manifolds of type A......Page 233
6. G.o. manifolds of type B......Page 236
7. General connection of type B......Page 238
References......Page 239
Conjugate connections and differential equations on infinite dimensional manifolds M. Aghasi, C. T. J. Dodson, G. N. Galanis and A. Suri......Page 240
1. Introduction......Page 241
2. Preliminaries......Page 242
3. Classification for vector bundle structures of T2M......Page 243
4. Connections and ordinary differential equations......Page 245
5. The Earle and Eells foliation theorem in Fréchet spaces......Page 248
References......Page 249
1. Introduction......Page 250
3. Totally biharmonic hypersurfaces......Page 251
4. Totally biharmonic surfaces of space forms......Page 254
5. Biharmonic curves in H3......Page 256
References......Page 258
1. Introduction......Page 260
2.1. Biharmonic maps......Page 261
2.2. The tangent bundle and the unit sphere bundle......Page 262
3. Homogeneous structures......Page 264
References......Page 268
1. Introduction......Page 270
2. Bihamonic maps and warped product manifolds......Page 271
3. Biharmonic submanifolds in space forms......Page 273
4. On the biharmonicity of the Gauss map......Page 276
References......Page 278
1. Introduction......Page 279
2. Preliminaries on contact pairs......Page 280
3.1. Almost contact structures......Page 281
3.2. Contact pair structures......Page 282
4. Compatible and associated metrics......Page 283
4.1. Orthogonal foliations......Page 287
References......Page 288
1. Introduction......Page 289
2. Paraquaternionic structures on manifolds......Page 290
3. Manifolds endowed with mixed 3-structures......Page 292
4. Normal semi-invariant submanifolds and mixed 3-structures......Page 295
Acknowledgements......Page 297
References......Page 298
2. An Extension of Myers' Theorem......Page 299
References......Page 303
1. Different types of Gray curvature conditions......Page 304
2. Gray curvature conditions for the Tanaka-Webster connection......Page 305
References......Page 307
1. Introduction......Page 309
2. Natural operators......Page 310
References......Page 313
1. Introduction......Page 314
2. The main result......Page 315
3. Proof of the main result......Page 317
References......Page 318
1. Introduction......Page 319
2. Geodesics on surfaces of revolution......Page 320
3. The Clairaut's relation......Page 322
References......Page 323
1. Introduction......Page 324
2. The quasi-constant holomorphic sectional curvatures of the cotangent bundles with general natural lifted metrics......Page 326
References......Page 328
1. Preliminaries......Page 329
2. Weingarten translation surfaces......Page 330
References......Page 333
1. Introduction and motivation......Page 334
2. The bundle of r-frames......Page 335
3. First order G-structures......Page 336
4. Second order G-structures......Page 337
References......Page 338
List of Participants......Page 340