Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224) - Tapa dura

Walschap, Gerald; Walschap, Gerard

 
9780387204307: Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics, 224)
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ISBN 10: 038720430X ISBN 13: 9780387204307
Editorial: Springer, 2004

Sinopsis

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines 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.

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De la contraportada

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.

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Editorial
Springer
Año de publicación
2004
Idioma
Inglés
ISBN 10 
038720430X
ISBN 13 
9780387204307
Encuadernación
Tapa dura
Número de páginas
244
Contacto del fabricante
no disponible
Persona responsable
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Otras ediciones populares con el mismo título

9781441919137: Metric Structures in Differential Geometry: 224 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1441919139 ISBN 13:  9781441919137
Editorial: Springer, 2010
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