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OverviewThis 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. Full Product DetailsAuthor: Joseph A. WolfPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: 6th Revised edition ISBN: 9781470473655ISBN 10: 1470473658 Pages: 420 Publication Date: 01 January 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsRiemannian geometry: Affine differential geometry Riemannian curvature The Euclidean space form problem: Flat Riemannian manifolds The spherical space form problem: Representations of finite groups Vincent's work on the spherical space form problem The classification of fixed point free groups The solution to the spherical space form problem Space form problems on symmetric spaces: Riemannian symmetric spaces Space forms of irreducible symmetric spaces Locally symmetric spaces of non-negative curvature Space form problems on indefinite metric manifolds: Spaces of constant curvature Locally isotropic manifolds Appendix to Chapter 12 References Additional references IndexReviewsAuthor InformationJoseph A. Wolf, University of California, Berkeley, CA. Tab Content 6Author Website:Countries AvailableAll regions |
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