# Riemannian Geometry

• Peter Petersen
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 171)

1. Front Matter
Pages i-xvi
2. Peter Petersen
Pages 1-18
3. Peter Petersen
Pages 19-61
4. Peter Petersen
Pages 63-88
5. Peter Petersen
Pages 89-102
6. Peter Petersen
Pages 103-136
7. Peter Petersen
Pages 137-162
8. Peter Petersen
Pages 163-205
9. Peter Petersen
Pages 207-242
10. Peter Petersen
Pages 243-271
11. Peter Petersen
Pages 273-315
12. Peter Petersen
Pages 317-359
13. Back Matter
Pages 361-434

### Introduction

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.

### Keywords

Riemannian geometry Spinor Tensor curvature manifold

#### Authors and affiliations

• Peter Petersen
• 1
1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-6434-5
• Copyright Information Springer-Verlag New York 1998
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-6436-9
• Online ISBN 978-1-4757-6434-5
• Series Print ISSN 0072-5285