Riemannian Geometry

Peter Petersen - Collection Graduate Texts in Mathematics

402 pages, parution le 01/12/2005 (2^eme édition)

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Résumé

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.

Important additions to this new edition include:

A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise;
An increased number of coordinate calculations of connection and curvature;
General fomulas for curvature on Lie Groups and submersions;
Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger;
Several recent results about manifolds with positive curvature.

Sommaire

Riemannian metric
Curvature
Examples
Hypersurfaces
Geodesics and distance
Sectional curvature comparison I
The Bochner technique
Symmetric spaces and holonomy
Ricci curvature comparison
Convergence
Sectional curvature comparison II
Appendix: De Rham cohomology

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Peter Petersen
Collection	Graduate Texts in Mathematics
Parution	01/12/2005
Édition	2^eme édition
Nb. de pages	402
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780387292465
ISBN13	978-0-387-29246-5