Riemannian Geometry - Paperback

by Peter Petersen (Author)

Designed for a one year introductory course, this volume introduces students to the important techniques and theorems of Riemannian geometry, while presenting sufficient background on advanced topics to appeal to students who wish to specialize in the discipline. The text combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and presents the most up-to-date research. The updated second edition includes such new material as: A completely new coordinate-free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; an expanded 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 forgotten proof by Berger; several recent results regarding manifolds with positive curvature.

Back Jacket

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