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OverviewThis volume provides an introduction to the geometry of manifolds equipped with additional structures connected with the notion of symmetry. Chapter I is concerned with the aspects of differential geometry which are used in subsequent chapters. Part of the chapter is devoted to general topology, part to the theory of smooth manifolds, and the remaining sections deal with manifolds with additional structures. Chapter II is devoted to the basic notions of the theory of spaces. One of the main topics here is the realization of affinely connected symmetric spaces as totally geodesic submanifolds of Lie groups. In Chapter IV, the most important classes of vector bundles are constructed. This is carried out in terms of differential forms. The geometry of the Euler class is of special interest here. Chapter V presents some applications of the geometrical concepts discussed. In particular, an introduction to modern methods of integration of nonlinear differential equations is given, as well as considerations involving the theory of hydrodynamic-type Poisson brackets with connections to interesting algebraic structures. It is designed for mathematicians and mathematical physicists wishing to obtain a good introduction to the geometry of manifolds. This volume can also be recommended as a supplementary graduate text. Full Product DetailsAuthor: V.V. Trofimov , G.G. OkunevaPublisher: Springer Imprint: Springer Edition: 1994 ed. Volume: 270 Dimensions: Width: 15.50cm , Height: 2.00cm , Length: 23.50cm Weight: 1.450kg ISBN: 9780792325611ISBN 10: 0792325613 Pages: 328 Publication Date: 28 February 1994 Audience: College/higher education , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback 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 ContentsI. Elements of differential geometry.- II. Lie Groups and Lie Algebras.- III. Symmetric spaces.- IV. Smooth vector bundles and characteristic classes.- V. Applications.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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