Geometry of Nonpositively Curved Manifolds (Chicago Lectures in Mathematics)

Starting from the foundations, the author presents an almost entirelyself-contained treatment of differentiable spaces of nonpositivecurvature, focusing on the symmetric spaces in which every geodesic liesin a flat Euclidean space of dimension at least two. The book builds toa discussion of the Mostow Rigidity Theorem and its generalizations, andconcludes by exploring the relationship in nonpositively curved spacesbetween geometric and algebraic properties of the fundamental group.This introduction to the geometry of symmetric spaces of non-compacttype will serve as an excellent guide for graduate students new to thematerial, and will also be a useful reference text for mathematiciansalready familiar with the subject.