Curvature in Mathematics and Physics (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Shlomo Sternberg

• Edition: Illustrated

• ISBN: 9780486478555

• Cover: Paperback

• Pages: 416

• Dimensions: 9.1 x 6.1 x 0.9 inches

• Release Date: 22-08-2012

About The Book
This comprehensive text is designed for advanced undergraduate and graduate students in mathematics and physics, focusing on differential geometry and its applications to general relativity. Written by renowned mathematician Shlomo Sternberg, it serves as both an introduction to semi-Riemannian geometry and a detailed exploration of its principal physical application—Einstein's theory of general relativity. The text employs Cartan's exterior calculus as the primary tool and includes essential topics like curvatures, linear connections, Levi-Civita's theorem, and variational formulas. Students will also delve into topics such as bi-invariant metrics, the Hopf-Rinow theorem, special and general relativity, and semi-Riemannian submersions. This book is ideal for those familiar with linear algebra and advanced calculus, particularly in the context of differential forms, offering a deep dive into both the mathematical foundations and physical implications of differential geometry.