Spaces of Constant Curvature: Sixth EditionShare 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.
Table of Contents
Table of Contents
Spaces of Constant Curvature: Sixth Edition
Graduate students and research mathematicians interested in riemannian geometry and homogeneous spaces of Lie groups.