| Document Type
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BL
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| Record Number
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846967
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| Main Entry
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Wolf, Joseph Albert,1936-
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| Title & Author
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Spaces of constant curvature /\ Joseph A. Wolf.
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| Edition Statement
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6th ed.
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| Publication Statement
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Providence, R.I. :: AMS Chelsea Pub.,, ©2011.
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| Page. NO
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xv, 420 pages :: illustrations ;; 27 cm
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| ISBN
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0821852825
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: 9780821852828
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Affine differential geometry -- Riemannian curvature -- Flat Riemannian manifolds -- 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 -- Rieman symmetric spaces -- Space forms of irreducible symmetric spaces -- Locally symmetric spaces of non-negative curvature -- Spaces of constant curvature -- Locally isotropic manifolds.
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| Abstract
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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.
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| Subject
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Geometry, Riemannian.
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Riemannian manifolds.
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Spaces of constant curvature.
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Symmetric spaces.
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Algebraic geometry-- Algebraic groups-- Classical groups (geometric aspects)
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Differential geometry-- Global differential geometry-- Homogeneous manifolds.
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Differential geometry-- Global differential geometry-- Lorentz manifolds, manifolds with indefinite metrics.
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Differential geometry-- Global differential geometry-- Methods of Riemannian geometry, including PDE methods; curvature restrictions.
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Differential geometry-- Global differential geometry-- Symmetric spaces.
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Differential geometry-- Research exposition (monographs, survey articles)
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Geometry, Riemannian.
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Group theory and generalizations-- Abstract finite groups-- None of the above, but in this section.
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Group theory and generalizations-- Representation theory of groups-- Group rings of finite groups and their modules.
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Nonassociative rings and algebras-- Lie algebras and Lie superalgebras-- Lie algebras of linear algebraic groups.
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Riemannian manifolds.
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Spaces of constant curvature.
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Symmetric spaces.
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Topological groups, Lie groups-- Compact groups-- Compact groups.
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| Dewey Classification
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516.3/73
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| LC Classification
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QA649.W64 2011
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| NLM classification
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20D99.msc
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53-0253C2153C3053C3553C5020C0522C0514L3517B4520D99msc
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