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Riemannian Geometry: A Modern Introduction by Isaac Chavel (City College, City University of New York) at Abbey's Bookshop,
Riemannian Geometry: A Modern Introduction
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Isaac Chavel (City College, City University of New York) B. Bollobas

Riemannian Geometry

A Modern Introduction

Isaac Chavel (City College, City University of New York),  B. Bollobas,  W. Fulton ,  A. Katok

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English
Cambridge University Press
10 April 2006
Mathematics & Sciences; Euclidean geometry; Differential & Riemannian geometry
Series: Cambridge Studies in Advanced Mathematics
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.
By:  
Series edited by:   , , ,
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Edition:   2nd Revised edition
Volume:   No. 98
Dimensions:   Height: 229mm,  Width: 152mm,  Spine: 25mm
Weight:   650g
ISBN:   9780521619547
ISBN 10:   0521619548
Series:   Cambridge Studies in Advanced Mathematics
Pages:   488
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
1. Riemannian manifolds; 2. Riemannian curvature; 3. Riemannian volume; 4. Riemannian coverings; 5. Surfaces; 6. Isoperimetric inequalities (constant curvature); 7. The kinetic density; 8. Isoperimetric inequalities (variable curvature); 9. Comparison and finiteness theorems.

Isaac Chavel is Professor of Mathematics at The City College of the City University of New York. He received his Ph.D. in Mathematics from Yeshiva University under the direction of Professor Harry E. Rauch. He has published in international journals in the areas of differential geometry and partial differential equations, especially the Laplace and heat operators on Riemannian manifolds. His other books include Eigenvalues in Riemannian Geometry, Academic Press, 1984, and Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives, Cambridge U. Press, 2001. He has been teaching at The City College of the City University of New York since 1970, and has been a member of the doctoral program of the City University of New York since 1976. He is a member of the American Mathematical Society.

Reviews for Riemannian Geometry: A Modern Introduction

'... 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.' SIAM Review


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