Differential Geometry: Bundles, Connections, Metrics and Curvature

Paperback | October 14, 2011

byClifford Henry Taubes

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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 Jacobifields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kahler 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 introductorymaterial is presented in full and this is the only such source with the classical examples presented in detail.

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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 di...

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 r...
Format:PaperbackDimensions:304 pages, 9.21 × 6.14 × 0.07 inPublished:October 14, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199605874

ISBN - 13:9780199605873

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Table of Contents

1. Smooth manifolds2. Matrices and Lie groups3. Introduction to vector bundles4. Algebra of vector bundles5. Maps and vector bundles6. Vector bundles with fiber Cn7. Metrics on vector bundles8. Geodesics9. Properties of geodesics10. Principal bundles11. Covariant derivatives and connections12. Covariant derivatives, connections and curvature13. Flat connections and holonomy14. Curvature polynomials and characteristic classes15. Covariant derivatives and metrics16. The Riemann curvature tensor17. Complex manifolds18. Holomorphic submanifolds, holomorphic sections and curvature19. The Hodge starIndexed list of propositions by subjectIndex