Riemannian Geometry: 171 - Brossura

Petersen, Peter

Brossura

ISBN 10: 1441921230 ISBN 13: 9781441921239

Casa editrice: Springer, 2010

Riassunto

This comprehensive introduction to Riemannian Geometry offers a detailed and engaging account of the topic, plus numerous exercises and examples. It combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and reviews the latest research.

Su questo libro

Recensione:

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)

Dalla quarta di copertina:

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

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2010
• ISBN 10: 1441921230
• ISBN 13: 9781441921239
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 424