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Graduate Texts in Mathematics

Riemannian Geometry

Authors: Petersen, Peter

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About this Textbook

This book is meant to be an introduction to Riemannian geometry. The reader is assumed to have some knowledge of standard manifold theory, including basic theory of tensors, forms, and Lie groups. At times we shall also assume familiarity with algebraic topology and de Rham cohomology. Specifically, we recommend that the reader is familiar with texts like [14] or[76, vol. 1]. For the readers who have only learned something like the first two chapters of [65], we have an appendix which covers Stokes' theorem, Cech cohomology, and de Rham cohomology. The reader should also have a nodding acquaintance with ordinary differential equations. For this, a text like [59] is more than sufficient. Most of the material usually taught in basic Riemannian geometry, as well as several more advanced topics, is presented in this text. Many of the theorems from Chapters 7 to 11 appear for the first time in textbook form. This is particularly surprising as we have included essentially only the material students ofRiemannian geometry must know. The approach we have taken deviates in some ways from the standard path. First and foremost, we do not discuss variational calculus, which is usually the sine qua non of the subject. Instead, we have taken a more elementary approach that simply uses standard calculus together with some techniques from differential equations.

Reviews

P. Petersen

Riemannian Geometry

"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."

—EUROPEAN MATHEMATICAL SOCIETY


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4757-6434-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
171
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-6434-5
DOI
10.1007/978-1-4757-6434-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
X, 198
Topics

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