Riemannian Geometry

Graduate Texts in Mathematics #171

by Peter Petersen

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

Genres: Mathematics, Geometry, Science

420 pages, Paperback

First published November 7, 1997

Reviews

[Colin Hinde · Rating 5 out of 5]

Will anyone on this website read this book based on my recommendation?

[Filip Dul · Rating 4 out of 5]

There are so many fantastic geometric expressions described in this book. The writing can be a bit dry—I wish the author would provide more intuition about certain facts—but this compendium should be on every differential geometer’s shelf.