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Oxford University Press
Differential Geometry: Bundles, Connections, Metrics and Curvature / Edition 1

Differential Geometry: Bundles, Connections, Metrics and Curvature / Edition 1

by Clifford Henry Taubes


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Product Details

ISBN-13: 9780199605873
Publisher: Oxford University Press
Publication date: 12/01/2011
Series: Oxford Graduate Texts in Mathematics Series , #23
Edition description: New Edition
Pages: 312
Product dimensions: 9.10(w) x 6.10(h) x 0.60(d)

About the Author

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.

Table of Contents

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 Cn
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

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