Metric Structures in Differential Geometry

Walschap Gerard

ISBN 10: 1441919139 / ISBN 13: 9781441919137

Published by Springer, 2010

About this Item

PRINT ON DEMAND pp. 240.

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Bibliographic Details

• Title: Metric Structures in Differential Geometry
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 1441919139
• ISBN 13: 9781441919137
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This text is an introduction to the theory of differentiable manifolds and fiber bundles. The only prerequisites are a solid background in calculus and linear algebra, together with some basic point-set topology.

From the Back Cover

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 of a 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.

Gerard Walschap is Professor of Mathematics at the University of Oklahoma where he developed this book for a series of graduate courses he has taught over the past few years.