Riemannian Geometry: 171 (Graduate Texts in Mathematics)

Book Details

• Author: Peter Petersen

• Publisher: Springer

• Binding: Paperback

• Number of Pages: 499

• Release Date: 24-04-2018

• ISBN: 9783319799896

• Package Dimensions: 9.1 x 6.0 x 1.1 inches

• Languages: English

About The Book
This book serves as an introduction to Riemannian geometry, making it an ideal resource for a one-year course on the subject. Peter Petersen combines both the geometric and analytic aspects of Riemannian geometry, providing a balanced approach to a complex field of mathematics. The text is designed to be accessible to readers who already have a basic understanding of standard manifold theory, including tensors, forms, and Lie groups, while also offering in-depth discussions for those who wish to specialize in Riemannian geometry.

The third edition has been significantly revised to include:

• A substantial addition of unique exercises that enrich the text, providing readers with a deeper understanding of the subject.

• An increased number of coordinate calculations for connection and curvature, helping students gain practical insight into Riemannian geometry.

• General formulas for curvature on Lie Groups and submersions, expanding the applicability of the material.

• Integration of variational calculus into the text, facilitating an early treatment of the Sphere theorem and a proof by Berger.

• Several recent developments in the study of manifolds with positive curvature, offering a modern perspective on the subject.

• A new simplifying approach to the Bochner technique for tensors, including applications to bound topological quantities under general lower curvature bounds.

Incorporating both foundational principles and recent advancements, this text is an invaluable resource for mathematicians and students looking to deepen their understanding of Riemannian geometry. It's highly recommended for anyone wishing to gain a comprehensive understanding of the subject and its applications.