Metric Structures in Differential Geometry

Gerard Walschap - Collection Graduate Texts in Mathematics

226 pages, parution le 11/05/2004

Ajouter à une liste

Indisponible

Résumé

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.

Written for:
Graduate students, mathematicians

Sommaire

Differentiable Manifolds
Fiber Bundles
Homotopy Groups and Bundles Over Spheres
Connections and Curvature
Metric Structures
Characteristic Classes

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Gerard Walschap
Collection	Graduate Texts in Mathematics
Parution	11/05/2004
Nb. de pages	226
Format	16 x 24
Couverture	Relié
Poids	530g
Intérieur	Noir et Blanc
EAN13	9780387204307
ISBN13	978-0-387-20430-7