Introduction to Geometry of Manifolds with Symmetry / Edition 1

by V.V. Trofimov

Overview

One of the most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour­ dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.

Product Details

ISBN-13:	9780792325611
Publisher:	Springer Netherlands
Publication date:	02/28/1994
Series:	Mathematics and Its Applications , #270
Edition description:	1994
Pages:	328
Product dimensions:	0.00(w) x 0.00(h) x 0.03(d)

Table of Contents

I. Elements of differential geometry.- II. Lie Groups and Lie Algebras.- III. Symmetric spaces.- IV. Smooth vector bundles and characteristic classes.- V. Applications.

Editorial Reviews

An introduction to the geometry of manifolds equipped with additional structures, connected with the notion of symmetry. The content is divided into five chapters: elements of differential geometry; Lie groups and Lie algebras; symmetric spaces; smooth vector bundles and characteristic classes; and applications. The volume is based on materials of special courses presented by the author to students of the Department of Mechanics and Mathematics at Moscow State University. For mathematicians and mathematical physicists, or as a supplementary graduate text. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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