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Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing) by Cheeger, Jeff; Ebin, D. G. is a nonfiction available to read on EtoBox.

What is Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing) about?

<p>The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem—the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is rela

Who reads Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing)?

Author

Cheeger, Jeff; Ebin, D. G.

Publisher

American Mathematical Society ; Oxford University Press [distributor

Published

2008

Language

EN

ISBN

9781470431211

Category

nonfiction

Subjects

Mathematics, Stem