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Riemannian Geometry: A Modern Introduction
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Type.................: Ebook
Part Size............: 2,596,904 bytes
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Posted by............: ~tqw~
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Release Notes
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This book provides an introduction to Riemannian geometry, the geometry of
curved spaces. Its main theme is the effect of the curvature of these spaces on
the usual notions of geometry - distances, areas, and volumes - and on those new
notions and ideas motivated by curvature itself. Among the more specialized
classical topics in a new setting are volume-comparison theorems, and
isoperimetric inequalities - the interplay of curvature with volume of sets and
the areas of their boundaries. Completely new themes created by curvature
include the interaction of microscopic behavior of the geometry with the
macroscopic structure of the space. After considering those topics which would
form the core of an introductory course, the book emphasizes more specialized
topics, here treated in book form for the first time. Also featured is a
nontraditional Notes and Exercises section for each chapter, to develop and
enrich the readers appetite for and appreciation of the subject.
Table of Contents
Preface
1 Riemannian manifolds 1
2 Riemannian curvature 49
3 Riemannian volume 101
4 Riemannian coverings 172
5 The kinematic density 219
6 Isoperimetric inequalities 262
7 Comparison and finiteness theorems 315
Hints and sketches of solutions 355
Bibliography 371
Index 383
Product Details
* ISBN: 0521853680
* ISBN-13: 9780521853682
* Format: Hardcover, 488pp
* Publisher: Cambridge University Press
* Pub. Date: March 2006
* Edition Description: REV
* Edition Number: 2
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