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25 Remote Warehouse Mathematics- Differential Geometry

This title in other editions

Geometry of Nonpositively Curved Manifolds (Chicago Lectures in Mathematics)

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Geometry of Nonpositively Curved Manifolds (Chicago Lectures in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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)

Description:

Includes bibliographical references (p. [429]-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

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

Product Details

ISBN:
9780226181981
Author:
Eberlein, Patrick
Publisher:
University of Chicago Press
Author:
Eberlein, Patrick B.
Location:
Chicago :
Subject:
Geometry - General
Subject:
Geometry - Differential
Subject:
Manifolds (mathematics)
Subject:
Manifolds
Subject:
Mathematics-Differential Geometry
Edition Description:
1
Series:
Chicago Lectures in Mathematics (Paperback)
Series Volume:
SP-520
Publication Date:
19970431
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
456
Dimensions:
9 x 6 in

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Related Subjects

Science and Mathematics » Mathematics » Differential Geometry
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