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  1. Home
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  3. Riemannian Geometry
  • Cited by 252
  • 2nd edition
  • Isaac Chavel, City College, City University of New York
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2006
Online ISBN:
9780511616822
DOI:
https://doi.org/10.1017/CBO9780511616822
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
Cambridge Studies in Advanced Mathematics (98)
Information

Book description

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.

Reviews

'… I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems. … an insightful modern perspective on topics of current research interest.'

Source: SIAM Review

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