Research Catalog

Title

Riemannian geometry / Peter Petersen.

Author

Petersen, Peter, 1962-

Publication

New York : Springer, ©2006.

Items in the Library & Off-site

Details

Description

xv, 401 pages : illustrations; 24 cm

Summary

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.

Series Statement

Graduate texts in mathematics ; 171

Uniform Title

Graduate texts in mathematics ; 171.

Subject

• Geometry, Riemannian
• Geometry, Riemannian
• Riemannsche Geometrie
• Geometria diferencial
• Geometria riemanniana

Note

• Earlier edition published in 1998.

Bibliography (note)

• Includes bibliographical references (p. 393-396) and index.

Contents

Riemannian metrics -- 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.

ISBN

• 0387292462
• 9780387292465
• 1441921230
• 9781441921239
• 9780387294032
• 0387294031

LCCN

• 2006923825
• 9780387292465
• 9781441921239

OCLC

• ocm71121685
• 71121685
• SCSB-1401677

Owning Institutions

Princeton University Library