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020			_a9780821852828
028			_a:Technical Bureau India Pvt. Ltd. _b:E/261, Shastri Nagar Delhi _c:TB345 _d:TB345
082			_a513.85 WOL
100			_aWolf, Joseph Albert
245			_aSpaces of Constant Curvature _c/ Joseph Albert Wolf
260			_aProvidence, R.I. _b: AMS Chelsea Pub _c©2011.
300			_axv, 420p. _b: illustrations _c; 27 cm
365			_b4746
505			_a 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.
520			_a 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.
650			_aMathematics
650			_aArithmetic
650			_aSpaces of constant curvature.
650			_aGeometry, Riemannian.
650			_aRiemannian manifolds.
650			_aDifferential geometry -- Global differential geometry -- Symmetric spaces.
650			_aDifferential geometry -- Global differential geometry -- Homogeneous manifolds.
650			_aDifferential geometry -- Global differential geometry -- Lorentz manifolds, manifolds with indefinite metrics.
650			_aAlgebraic geometry -- Algebraic groups -- Classical groups (geometric aspects)
650			_aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Lie algebras of linear algebraic groups.
650			_aDifferential geometry -- Research exposition (monographs, survey articles)
650			_aRiemannian manifolds.
700			_aWolf, Joseph Albert,
942			_cBOOK
999			_c59205 _d59205