{"product_id":"spaces-of-constant-curvature-9781470473655","title":"Spaces of Constant Curvature","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eRiemannian geometry: Affine differential geometry\u003c\/li\u003e\n\u003cli\u003eRiemannian curvature\u003c\/li\u003e\n\u003cli\u003eThe Euclidean space form problem: Flat Riemannian manifolds\u003c\/li\u003e\n\u003cli\u003eThe spherical space form problem: Representations of finite groups\u003c\/li\u003e\n\u003cli\u003eVincent's work on the spherical space form problem\u003c\/li\u003e\n\u003cli\u003eThe classification of fixed point free groups\u003c\/li\u003e\n\u003cli\u003eThe solution to the spherical space form problem\u003c\/li\u003e\n\u003cli\u003eSpace form problems on symmetric spaces: Riemannian symmetric spaces\u003c\/li\u003e\n\u003cli\u003eSpace forms of irreducible symmetric spaces\u003c\/li\u003e\n\u003cli\u003eLocally symmetric spaces of non-negative curvature\u003c\/li\u003e\n\u003cli\u003eSpace form problems on indefinite metric manifolds: Spaces of constant curvature\u003c\/li\u003e\n\u003cli\u003eLocally isotropic manifolds\u003c\/li\u003e\n\u003cli\u003eAppendix to Chapter 12\u003c\/li\u003e\n\u003cli\u003eReferences\u003c\/li\u003e\n\u003cli\u003eAdditional references\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046688821591,"sku":"9781470473655","price":48.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470473655.jpg?v=1740272273","url":"https:\/\/bookcurl.com\/products\/spaces-of-constant-curvature-9781470473655","provider":"Book Curl","version":"1.0","type":"link"}