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Riemannian Geometry

  • Peter┬áPetersen

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

Table of contents

  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

About this book

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┬áPetersen
    • 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 Springer Book Archive
  • Print ISBN 978-1-4757-6436-9
  • Online ISBN 978-1-4757-6434-5
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site