Comparison Theorems in Riemannian Geometry

2008/04/08 by Jeff Cheeger, David G. Ebin · 7 citations
Mathematics · #Geometry #Mathematics #Morphological variations and asymmetry #Physics #Riemannian geometry

paper · doi:10.1090/chel/365

openalex publication_date 2008/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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 re

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