Differential Geometry : Proceedings of the VIII International Colloquium

by Lopez, Jesus a Alvarez; Garcia-Rio, Eduardo

• ISBN13: 9789814261166
• ISBN10: 9814261165
• Format: Hardcover
• Copyright: 2009-04-27
• Publisher: World Scientific Pub Co Inc

Summary

This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps. Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and ThurstonBennequin's inequalities, a discussion about FatouJulia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points. Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.

Table of Contents

Preface	p. v
Organizing Committees	p. vii
A brief portrait of the life and work of Professor Enrique Vidal Abascal	p. 1
Foliation theory	p. 9
Characteristic classes for Riemannian foliations	p. 11
Non unique-ergodicity of harmonic measures: Smoothing Samuel Petite's examples	p. 36
On the uniform simplicity of diffeomorphism groups	p. 43
On Bennequin's isotopy lemma and Thurston's inequality	p. 56
On the Julia sets of complex codimension-one transversally holomorphic foliations	p. 65
Singular Riemannian foliations on spaces without conjugate points	p. 75
Variational formulate for the total mean curvatures of a codimension-one distribution	p. 83
On a Weitzenböet;ck-like formula for Riemannian foliations	p. 94
Duality and minimality for Riemannian foliations on open manifolds	p. 102
Open problems on foliations	p. 104
Riemannian geometry	p. 109
Graphs with prescribed mean curvature	p. 111
Genuine isometric and conformal deformations of submanifolds	p. 120
Totally geodesic submanifolds in Riemannian symmetric spaces	p. 136
The orbits of cohomogeneity one actions on complex hyperbolic spaces	p. 146
Rigidity results for geodesic spheres in space forms	p. 156
Mean curvature flow and Bernstein-Calabi results for spacelike graphs	p. 164
Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators	p. 175
Conformally Osserman multiply warped product structures in the Riemannian setting	p. 185
Riemannian ¿-symmetric spaces	p. 195
Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank	p. 207
On the reparametrization of affine homogeneous geodesics	p. 217
Conjugate connections and differential equations on infinite dimensional manifolds	p. 227
Totally biharmonic submanifolds	p. 237
The biharmonicity of unit vector fields on the Poincaré half-space Hn	p. 247
Prespectives on biharmonic maps and submanifolds	p. 257
Contact pair structures and associated metrics	p. 266
Paraquaternionic manifolds and mixed 3-structures	p. 276
On topological obstruction of compact positively Ricci curved manifolds	p. 286
Gray curvature conditions and the Tanaka-Webster connection	p. 291
Riemannian structures on higher order frame bundles from classical linear connections	p. 296
Distributions on the cotangent bundle from torsion-free connections	p. 301
On the geodesics of the rotational surfaces in the Bianchi-Cartan-Vranceanu spaces	p. 306
Cotangent bundles with general natural Käet;hler structures of quasi-constant holomorphic sectional curvatures	p. 311
Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space	p. 316
G-structures defined on pseudo-Riemannian manifolds	p. 321
List of Participants	p. 327
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