Introduction to Geometry of Manifolds with Symmetry by V.V. TrofimovIntroduction to Geometry of Manifolds with Symmetry by V.V. Trofimov

Introduction to Geometry of Manifolds with Symmetry

byV.V. Trofimov

Paperback | December 5, 2010

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This volume provides an introduction to the geometry of manifolds equipped with additional structures connected with the notion of symmetry. The content is divided into five chapters. Chapter I presents the elements 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. 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.
Title:Introduction to Geometry of Manifolds with SymmetryFormat:PaperbackDimensions:339 pages, 10.98 × 8.27 × 0 inPublished:December 5, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048143365

ISBN - 13:9789048143368

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Table of Contents

Notation. Preface. I: Elements of Differential Geometry. II: Lie Groups and Lie Algebras. III: Symmetric Spaces. IV: Smooth Vector Bundles and Characteristic Classes. V: Applications. Index. Bibliography.