Riemannian Geometry

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Riemannian Geometry

By Isaac Chavel

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This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Subject: Mathematics & Statistics -> Post-Calculus -> Topology

Riemannian Geometry
A Modern Introduction
2nd edition
Publisher: Cambridge University Press 4/10/06
Imprint: Cambridge University Press
Language: English

ISBN 10: 0511217811
ISBN 13: 9780511217814
Print ISBN: 9780521853682

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