Ams Chelsea Publishing: Comparison Theorems in Riemannian Geometry (Other)

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.