Global Riemannian Geometry: Curvature and Topology

The book contains a clear exposition of two contemporary topics in modern differential geometry:- distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature- the application of the Lichnerowicz formula for Dirac operators to the study of Gromov’s invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers who want to get a quick and modern introduction to these topics.