Introduction to Geometry of Manifolds with Symmetry (Hardcover, 1994 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 270
Release date:	February 1994
First published:	1994
Authors:	V.V. Trofimov
Dimensions:	235 x 155 x 20mm (L x W x T)
Format:	Hardcover
Pages:	328
Edition:	1994 ed.
ISBN-13:	978-0-7923-2561-1
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	0-7923-2561-3
Barcode:	9780792325611

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