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.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
AMS Chelsea Publishing |
Release date: |
2011 |
Authors: |
Joseph A. Wolf
|
Pages: |
420 |
Edition: |
6th Revised edition |
ISBN-13: |
978-1-4704-7365-5 |
Categories: |
Books
|
LSN: |
1-4704-7365-8 |
Barcode: |
9781470473655 |
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