Differential Geometry: Proceedings of the Viii International Colloquium

Differential Geometry: Proceedings of the Viii International Colloquium

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World Scientific Publishing Company, Incorporated


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Differential Geometry: Proceedings of the Viii International Colloquium

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 Thurston-Bennequin's inequalities, a discussion about Fatou-Julia 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.

Product Details

ISBN-13: 9789814261166
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 08/28/2009
Pages: 344
Product dimensions: 6.20(w) x 9.00(h) x 1.00(d)

Table of Contents

Preface v

Organizing Committees vii

A brief portrait of the life and work of Professor Enrique Vidal Abascal L. A. Cordero 1

Part A Foliation theory 9

Characteristic classes for Riemannian foliations S. Hurder 11

Non unique-ergodicity of harmonic measures: Smoothing Samuel Petite's examples B. Deroin 36

On the uniform simplicity of diffeomorphism groups T. Tsuboi 43

On Bennequin's isotopy lemma and Thurston's inequality Y. Mitsumatsu 56

On the Julia sets of complex codimension-one transversally holomorphic foliations T. Asuke 65

Singular Riemannian foliations on spaces without conjugate points A. Lytchak 75

Variational formulate for the total mean curvatures of a codimension-one distribution V. Rovenski P. Walczak 83

On a Weitzenböet;ck-like formula for Riemannian foliations V. Slesar 94

Duality and minimality for Riemannian foliations on open manifolds X. M. Masa 102

Open problems on foliations 104

Part B Riemannian geometry 109

Graphs with prescribed mean curvature M. Dajczer 111

Genuine isometric and conformal deformations of submanifolds R. Tojeiro 120

Totally geodesic submanifolds in Riemannian symmetric spaces S. Klein 136

The orbits of cohomogeneity one actions on complex hyperbolic spaces J. C. Díaz-Ramos 146

Rigidity results for geodesic spheres in space forms J. Roth 156

Mean curvature flow and Bernstein-Calabi results for spacelike graphs G. Li I. M. C. Salavessa 164

Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators P. Gilkey S. Nik&ccheck;ević D. Westerman 175

Conformally Osserman multiply warped product structures in the Riemannian setting M. Brozos-VázquezM. E. Vázquez-Abal R. Vázquez-Lorenzo 185

Riemannian τ-symmetric spaces M. Goze E. Remm 195

Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank T. Arias-Marco 207

On the reparametrization of affine homogeneous geodesics Z. Du&scheck;ek 217

Conjugate connections and differential equations on infinite dimensional manifolds M. Aghasi C. T. J. Dodson G. N. Galanis A. Suri 227

Totally biharmonic submanifolds D. Impera S. Montaldo 237

The biharmonicity of unit vector fields on the Poincaré half-space Hn M. K. Markellos 247

Prespectives on biharmonic maps and submanifolds A. Balmu&scidle; 257

Contact pair structures and associated metrics G. Bande A. Hadjar 266

Paraquaternionic manifolds and mixed 3-structures S. Ianu&scidle; G. E. V&icheck;lcu 276

On topological obstruction of compact positively Ricci curved manifolds W.-H. Chen 286

Gray curvature conditions and the Tanaka-Webster connection R. Mocanu 291

Riemannian structures on higher order frame bundles from classical linear connections J. Kurek W. M. Mikulski 296

Distributions on the cotangent bundle from torsion-free connections J. Kurek W. M. Mikulski 301

On the geodesics of the rotational surfaces in the Bianchi-Cartan-Vranceanu spaces P. Piu M. M. Profir 306

Cotangent bundles with general natural Käet;hler structures of quasi-constant holomorphic sectional curvatures S. L. Dru&tcidle;&acheck; 311

Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space M. I. Munteanu A. I. Nistor 316

G-structures defined on pseudo-Riemannian manifolds I. Sánchez-Rodríguez 321

List of Participants 327

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