Geometry of Nonpositively Curved Manifolds (Chicago Lectures in Mathematics)

self-contained treatment of differentiable spaces of nonpositive

curvature, focusing on the symmetric spaces in which every geodesic lies

in a flat Euclidean space of dimension at least two. The book builds to

a discussion of the Mostow Rigidity Theorem and its generalizations, and

concludes by exploring the relationship in nonpositively curved spaces

between geometric and algebraic properties of the fundamental group.

This introduction to the geometry of symmetric spaces of non-compact

type will serve as an excellent guide for graduate students new to the

material, and will also be a useful reference text for mathematicians

already familiar with the subject.

Introduction

1. Notation and Preliminaries

2. Structure of Symmetric Spaces of Noncompact Type

3. Tits Geometries

4. Action of Isometrics on M(infinity)

5. A Splitting Criterion

6. Isometries of R"

7. Spaces with Euclidean Factors

8. Mostow Rigidity Theorem

9. Rigidity Theorems and Characterizations of Symmetric Spaces of Higher Rank

10. Fundamental Group and Geometry

References

Index of Definitions and Terminology

Index of Notation