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Graduate Texts in Mathematics

Riemannian Geometry

Authors: Petersen, Peter

  • A comprehensive introduction to Riemannian Geometry
  • Offers a detailed and engaging description of the topic
  • Includes numerous exercises and examples
  • Presents several theorems for the first time in textbook form
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eBook $49.99
price for USA (gross)
  • ISBN 978-0-387-29403-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $64.95
price for USA
  • ISBN 978-1-4419-2123-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

Reviews

From the reviews of the second edition:

P. Petersen

Riemannian Geometry

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

—EUROPEAN MATHEMATICAL SOCIETY

“This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. … After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner–Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)


Table of contents (16 chapters)

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-0-387-29403-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $64.95
price for USA
  • ISBN 978-1-4419-2123-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
171
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-29403-2
DOI
10.1007/978-0-387-29403-2
Softcover ISBN
978-1-4419-2123-9
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XV, 405
Topics