Differential geometry, Valencia 2001 : proceedings of the international conference held to honour the 60th birthday of A.M. Naveira, Valencia, July 8-14, 2001 / editors, Olga Gil-Medrano, Vicente Miquel.

Format:

Book

Contributor:

Gil-Medrano, O. (Olga)

Miquel, Vicente.

Naveira, A. M. (Antonio Martínez), 1940-

Language:

English

Subjects (All):

Geometry, Differential--Congresses.

Geometry, Differential.

Global differential geometry--Congresses.

Global differential geometry.

Physical Description:

1 online resource (324 p.)

Place of Publication:

River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore-Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with fin

Contents:

Preface; List of Participants; Contents; A Tour on the Life and Work of A. M. Naveira; 1 Introduction; 2 Some biographical data of A. M. Naveira; 3 Naveira at Santiago by L. Hervella; 4 Naveira at Granada and Valencia by A. Ferrandez; 5 Mathematical activity of Prof. Naveira; Some Rigidity Results for Compact Spacelike Surfaces in the 3-dimensional de Sitter Space; 1 Introduction; 2 Preliminaries; 3 Surfaces with a constant principal curvature; 4 Linear Weingarten Surfaces; References; Hypersurfaces with Constant Higher Order Mean Curvature in Euclidean Space; 1 Introduction

2 A classical result: the Alexandrov theorem3 Elliptic equations and maximum principles; 4 Alexandrov's reflection method; 5 Reilly's method; 6 The Alexandrov theorem for higher order mean curvatures; 7 A volume estimate in terms of the mean curvature. Ros' proof of Theorem 5; 8 A maximum principle for constant higher order mean curvature. Korevaar's proof of Theorem 5; 9 The case of non-empty boundary; 10 The Newton transformations; 11 A geometric configuration; 12 A flux formula; 13 Rosenberg's proof of Theorem 12; 14 Transversality versus ellipticity. Proof of Theorem 13; References

Uniqueness of Spacelike Hypersurfaces with Constant Mean Curvature in Generalized Robertson-Walker Spacetimes1 Introduction; 2 Preliminaries; 3 Compact spacelike hypersurfaces; 4 Complete spacelike hypersurfaces; References; Best Inequalities of Sobolev Type on Complete Riemannian Manifolds; Critical Points of Willmore-Chen Tension Functionals; 1 Motivation; 2 Willmore functionals; 3 The inverse Kaluza-Klein mechanism; 4 Appendix: The Principle of Symmetric Criticality (R.S. Palais); 5 Willmore Tori via reduction of variables; 6 Examples and Applications; 7 Further Applications; References

Some Generalizations of Twistor Spaces1 Introduction and classical twistor spaces.; 2 A hyperbolic twistor space.; 3 A product twistor space.; 4 The twistor space of a quaternionic 3-symmetric manifold.; References; Biharmonic Immersions into Spheres; 1 Introduction; 2 Biharmonic Maps; 3 Biharmonic curves in S3; 4 Biharmonic submanifolds in Sn; References; The Gauss Map Spacelike Rotational Surfaces with Constant Mean Curvature in the Lorentz-Minkowski Space; 1 Introduction; 2 Preliminaries; 3 Surfaces of revolution with spacelike axis; 4 Surfaces of revolution with timelike axis

5 Surfaces of revolution with lightlike axisReferences; The Intrinsic Torsion of SU(3) and G2 Structures; Introduction; 1 Static SU(3) structures; 2 Static G 2 structures; 3 Product manifolds; 4 Dynamic G2 structures; 5 Fibred G2 manifolds; References; H-Hypersurfaces with Finite Total Curvature; 1 Introduction: historical perspective; 2 Finite total curvature for complete .ff-hypersurfaces. Topological structure; 3 Complete H-hypersurfaces with finite total curvature. Further results.; References; Null Helices and Degenerate Curves in Lorentzian Spaces; 1 Introduction

2 The Cartan frame of a null curve

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611929794

9781281929792

1281929794

9789812777751

981277775X