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Introduction to Geometry of Manifolds with Symmetry : Mathematics and Its Applications - V.V. Trofimov

Introduction to Geometry of Manifolds with Symmetry

Mathematics and Its Applications

Hardcover Published: 28th February 1994
ISBN: 9780792325611
Number Of Pages: 328

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This 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.

Notation
Preface
Elements of Differential Geometry
Lie Groups and Lie Algebras
Symmetric Spaces
Smooth Vector Bundles and Characteristic Classes
Applications
Index
Bibliography
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792325611
ISBN-10: 0792325613
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 328
Published: 28th February 1994
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.06
Weight (kg): 0.66

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