Riemannian Geometry (v. 171) [Hardcover]

Peter Petersen (Author)

Book Description

ISBN-10: 0387982124 | ISBN-13: 978-0387982120 | Publication Date: November 7, 1997 | Edition: 1

This book is intended for a one year course in Riemannian Geometry. It will serve 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. Instead of variational techniques, the author uses a unique approach emphasizing distance functions and special coordinate systems. He also uses standard calculus with some techniques from differential equations, instead of variational calculus, thereby providing a more elementary route for students. Many of the chapters contain material typically found in specialized texts and never before published together in one source. Key sections include noteworthy coverage of: geodesic geometry, Bochner technique, symmetric spaces, holonomy, comparison theory for both Ricci and sectional curvature, and convergence theory. This volume is one of the few published works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory as well as presenting the most up-to-date research including sections on convergence and compactness of families of manifolds. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help to motivate readers to deepen their understanding of the subject.

Editorial Reviews

Review

P. Petersen

Riemannian Geometry

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

—EUROPEAN MATHEMATICAL SOCIETY

Product Details

• Hardcover: 416 pages
• Publisher: Springer; 1 edition (November 7, 1997)
• Language: English
• ISBN-10: 0387982124
• ISBN-13: 978-0387982120
• Product Dimensions: 9.4 x 6.3 x 1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,994,780 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

5 of 12 people found the following review helpful:

4.0 out of 5 stars Hard to say, February 9, 2008

By 

Ronald Reagan - See all my reviews

This review is from: Riemannian Geometry (Universitext) (Paperback)

This was the official 100% recommended, guaranteed text for my Riemannian Geometry class. Supplementing this book with do Carmo's text, I was able to get something out of the class, but I think rereading both of them now would be much better. The condensed one chapter course on manifolds at the beginning of GHL wasn't sufficient to learn/relearn everything I needed to know in order to read it for the first time.