Description

Book Synopsis
Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature.

Table of Contents
Basic concepts and results Toponogov's theorem Homogeneous spaces Morse theory Closed geodesics and the cut locus The sphere theorem and its generalizations The differentiable sphere theorem Complete manifolds of nonnegative curvature Compact manifolds of nonpositive curvature Bibliography Additional bibliography Index.

Comparison Theorems in Riemannian Geometry

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    A Hardback by Jeffrey Cheeger

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      View other formats and editions of Comparison Theorems in Riemannian Geometry by Jeffrey Cheeger

      Publisher: MP-AMM American Mathematical
      Publication Date: 4/30/2008 12:00:00 AM
      ISBN13: 9780821844175, 978-0821844175
      ISBN10: 0821844172

      Description

      Book Synopsis
      Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature.

      Table of Contents
      Basic concepts and results Toponogov's theorem Homogeneous spaces Morse theory Closed geodesics and the cut locus The sphere theorem and its generalizations The differentiable sphere theorem Complete manifolds of nonnegative curvature Compact manifolds of nonpositive curvature Bibliography Additional bibliography Index.

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