Geometry of Nonpositively Curved Manifolds

by Patrick B. Eberlein

Overview

Starting from the foundations, the author presents an almost entirely
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.

Product Details

ISBN-13:	9780226181981
Publisher:	University of Chicago Press
Publication date:	04/01/1997
Series:	Chicago Lectures in Mathematics
Edition description:	1
Pages:	456
Product dimensions:	6.00(w) x 9.00(h) x 1.20(d)

About the Author

Patrick B. Eberlein is professor of mathematics at the University of North Carolina at Chapel Hill.

Table of Contents

Acknowledgments
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