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Differential geometry : bundles, connections, metrics and curvature

Author: Clifford Taubes
Publisher: Oxford ; New York : Oxford University Press, ©2011.
Series: Oxford mathematics.; Oxford graduate texts in mathematics, 23.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.
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Document Type: Book
All Authors / Contributors: Clifford Taubes
ISBN: 0199605882 9780199605880 9780199605873 pbk.) 0199605874
OCLC Number: 760133929
Description: xiii, 298 pages : illustrations ; 24 cm.
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 C[superscript n] as fiber --
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.
Series Title: Oxford mathematics.; Oxford graduate texts in mathematics, 23.
Responsibility: Clifford Henry Taubes.

Abstract:

Bundles, connections, metrics & curvature are the lingua franca of modern differential geometry & theoretical physics. Supplying graduate students in mathematics or theoretical physics with the  Read more...

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"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 Read more...

 
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