**AMS Chelsea Publishing**

Volume: 372;
2011;
420 pp;
Hardcover

MSC: Primary 53; 20; 22;
Secondary 14; 17

Print ISBN: 978-0-8218-5282-8

Product Code: CHEL/372.H

List Price: $60.00

Individual Member Price: $54.00

**Electronic ISBN: 978-1-4704-1579-2
Product Code: CHEL/372.H.E**

List Price: $60.00

Individual Member Price: $48.00

#### Supplemental Materials

# Spaces of Constant Curvature: Sixth Edition

Share this page
*Joseph A. Wolf*

This book is the sixth edition of the classic Spaces of Constant
Curvature, first published in 1967, with the previous (fifth) edition
published in 1984. It illustrates the high degree of interplay between
group theory and geometry. The reader will benefit from the very concise
treatments of riemannian and pseudo-riemannian manifolds and their
curvatures, of the representation theory of finite groups, and of
indications of recent progress in discrete subgroups of Lie groups.

Part I is a brief introduction to differentiable manifolds, covering
spaces, and riemannian and pseudo-riemannian geometry. It also contains a
certain amount of introductory material on symmetry groups and space
forms, indicating the direction of the later chapters. Part II is an
updated treatment of euclidean space form. Part III is Wolf's classic
solution to the Clifford–Klein Spherical Space Form Problem. It starts
with an exposition of the representation theory of finite groups. Part IV
introduces riemannian symmetric spaces and extends considerations of
spherical space forms to space forms of riemannian symmetric spaces.
Finally, Part V examines space form problems on pseudo-riemannian
symmetric spaces. At the end of Chapter 12 there is a new appendix
describing some of the recent work on discrete subgroups of Lie groups
with application to space forms of pseudo-riemannian symmetric spaces.
Additional references have been added to this sixth edition as well.

#### Readership

Graduate students and research mathematicians interested in riemannian geometry and homogeneous spaces of Lie groups.

#### Table of Contents

# Table of Contents

## Spaces of Constant Curvature: Sixth Edition

- Cover Cover11
- Title page iii4
- Dedication v6
- Preface vii8
- Preface to the sixth edition x11
- Notes to the reader xi12
- Contents xiii14
- Riemannian geometry 120
- Affine differential geometry 120
- Riemannian curvature 4564
- The Euclidean space form problem 97116
- Flat Riemannian manifolds 98117
- The spherical space form problem 137156
- Representations of finite groups 138157
- Vincent’s work on the spherical space form problem 154173
- The classification of fixed point free groups 172191
- The solution to the spherical space form problem 198217
- Space form problems on symmetric spaces 231250
- Riemannian symmetric spaces 231250
- Space forms of irreducible symmetric spaces 303322
- Locally symmetric spaces of non-negative curvature 328347
- Space form problems on indefinite metric manifolds 337356
- Spaces of constant curvature 337356
- Locally isotropic manifolds 374393
- Appendix to Chapter 12 396415
- References 402421
- Additional references 408427
- Index 413432
- Back Cover Back Cover1442