Differential Geometry: Bundles, Connections, Metrics and Curvature

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Clifford Henry Taubes (William Petschek Professor of Mathematics, Harvard University)

Differential Geometry

Bundles, Connections, Metrics and Curvature

Clifford Henry Taubes (William Petschek Professor of Mathematics, Harvard University)

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English

Oxford University Press
24 March 2011

Differential & Riemannian geometry; Algebraic topology; Particle & high-energy physics; Mathematical physics

Series: Oxford Graduate Texts in Mathematics

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. 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.

Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.

By: Clifford Henry Taubes (William Petschek Professor of Mathematics Harvard University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 23
Dimensions: Height: 232mm, Width: 155mm, Spine: 26mm
Weight: 1g
ISBN: 9780199605880
ISBN 10: 0199605882
Series: Oxford Graduate Texts in Mathematics
Pages: 312
Publication Date: 24 March 2011
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

1: Smooth manifolds 2: Matrices and Lie groups 3: Introduction to vector bundles 4: Algebra of vector bundles 5: Maps and vector bundles 6: Vector bundles with fiber C]n 7: Metrics on vector bundles 8: Geodesics 9: Properties of geodesics 10: Principal bundles 11: Covariant derivatives and connections 12: Covariant derivatives, connections and curvature 13: Flat connections and holonomy 14: Curvature polynomials and characteristic classes 15: Covariant derivatives and metrics 16: The Riemann curvature tensor 17: Complex manifolds 18: Holomorphic submanifolds, holomorphic sections and curvature 19: The Hodge star Indexed list of propositions by subject Index

Clifford Henry Taubes is the William Petschek Professor of Mathematics at Harvard University. He is a member of the National Academy of Sciences and also the American Academy of Sciences. He was awarded the American Mathematical Society's Oswald Veblen Prize in 1991 for his work in differential geometry and topology. He was also the recipient of the French Academy of Sciences Elie Cartan Prize in 1993, the Clay Research Award in 2008, the National Academy of Sciences' Mathematics Award in 2008, and the Shaw Prize in Mathematics in 2009.

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

"""Taube's proofs are wonderful, complete and elegant... He is clear and concise, and indeed presents all the material beautifully and in a self contained manner, to the degree possible. ... He amplifies everything with generous allusions to other sources so that the reader is easily able to follow up on certain themes with considerable ease."" --MAA Reviews"