Riemannian Geometry

  • Peter┬áPetersen
Part of the Graduate Texts in Mathematics book series (GTM, volume 171)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Pages 1-19
  3. Pages 21-62
  4. Pages 63-93
  5. Pages 95-109
  6. Pages 111-151
  7. Pages 187-234
  8. Pages 293-332
  9. Back Matter
    Pages 375-405

About this book

Introduction

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.

Important additions to this new edition include:

* A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise;

* An increased number of coordinate calculations of connection and curvature;

* General fomulas for curvature on Lie Groups and submersions;

* Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger;

* Several recent results about manifolds with positive curvature.

From reviews of the first edition:

"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."

- Bernd Wegner, Zentralblatt

Keywords

Riemannian geometry Submersion 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/10.1007/978-0-387-29403-2
  • Copyright Information Springer Science + Business Media, LLC 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-29246-5
  • Online ISBN 978-0-387-29403-2
  • Series Print ISSN 0072-5285
  • About this book