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Differential Geometry
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Differential Geometry: Bundles, Connections, Metrics and Curvature

Clifford Henry Taubes

Abstract

Bundles, connections, metrics, and curvature are the ‘lingua franca’ of modern differential geometry and theoretical physics. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. The book uses many of ... More

Keywords: bundles, metrics, curvature, differential geometry, theoretical physics, differential topology, differentiable manifolds, smooth maps, differential forms, vector fields

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780199605880
Published to Oxford Scholarship Online: December 2013 DOI:10.1093/acprof:oso/9780199605880.001.0001

Authors

Affiliations are at time of print publication.

Clifford Henry Taubes, author
William Petschek Professor of Mathematics, Harvard University