Metric Structures in Differential Geometry Hardcover - 2004
by Gerard Walschap
First line
Recall that the vector space Rn is the set ((p1,...,pn) | p1 R), together with coordinate-wise addition and scalar multiplication.
From the rear 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.
Details
- Title Metric Structures in Differential Geometry
- Author Gerard Walschap
- Binding Hardcover
- Edition FALSE
- Pages 229
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2004-03-18
- Illustrated Yes
- ISBN 9780387204307 / 038720430X
- Weight 1.14 lbs (0.52 kg)
- Dimensions 9.21 x 6.14 x 0.56 in (23.39 x 15.60 x 1.42 cm)
- Library of Congress subjects Geometry, Differential
- Library of Congress Catalog Number 2003066219
- Dewey Decimal Code 516.36
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Metric Structures in Differential Geometry (Graduate Texts in Mathematics 224)
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