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Metric Structures in Differential Geometry

Name: Metric Structures in Differential Geometry
Brand: Springer, Berlin
SKU: 01380910
Price: 38694 HUF
Availability: InStock
Author: Gerard Walschap
ISBN: 9780387204307

Gerard Walschap

Language

English

Book Hardback

Libristo code: 01380910

Publishers Springer, Berlin, November 2003

This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only r... Full description

Libristo code: 01380910

259 b

38 694 Ft

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This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only requisites are a solid background in calculus and linear algebra, together with some basic point-set topology. The first chapter provides a comprehensive overview of differentiable manifolds. The following two chapters are devoted to fiber bundles and homotopy theory of fibrations. Vector bundles have been emphasized, although principal bundles are also discussed in detail. The last three chapters study bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes ofa vector bundle. These concepts are illustrated in detail for bundles over spheres. Chapter 5, with its focus on the tangent bundle, also serves as a basic introduction to Riemannian geometry in the large. This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry.