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Geometry of Nonpositively Curved Manifolds (Chicago Lectures in Mathematics)by Patrick Eberlein
Synopses & Reviews
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.
Book News Annotation:
A graduate level reference text introducing the geometry of symmetric spaces of noncompact type. Eberlein (mathematics, U. of North Carolina, Chapel Hill) gives a self-contained treatment of differentiable spaces of nonpositive curvature, focusing on higher rank symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two, and proof of Mostow's Rigidy Theorem in the higher rank case rewritten in differential geometric language and describing several differential geometric characterizations of higher rank symmetric spaces arising from the theorem's generalizations. The author concludes with a discussion of the relationship between the geometric properties of nonpositively curved spaces and algebraic properties of their fundamental groups.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Includes bibliographical references (p. -436) and indexes.
About the Author
Patrick B. Eberlein is professor of mathematics at the University of North Carolina at Chapel Hill.
Table of Contents
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
Index of Definitions and Terminology
Index of Notation
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