Metric Structures in Differential Geometry

Gerard Walschap

ISBN 10: 1441919139 / ISBN 13: 9781441919137

Published by Humana, 2010

About this Item

Metric Structures in Differential Geometry | Gerard Walschap | Taschenbuch | viii | Englisch | 2010 | Humana | EAN 9781441919137 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 107253293

Bibliographic Details

• Title: Metric Structures in Differential Geometry
• Publisher: Humana
• Publication Date: 2010
• Language: English
• ISBN 10: 1441919139
• ISBN 13: 9781441919137
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 14D millimeters 235 millimeters width by 155 millimeters height by 14 millimeters depth
• Weight: 371 grams
• Seller catalogs:
  • Bücher

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.