Differential geometry : bundles, connections, metrics and curvature / Clifford Henry Taubes.

Format:

Book

Author/Creator:

Taubes, Clifford, 1954- author.

Series:

Oxford graduate texts in mathematics ; 23.

Oxford graduate texts in mathematics ; 23

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

1 online resource (313 p.)

Place of Publication:

Oxford : Oxford University Press, 2011.

Language Note:

English

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.

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-162178-1

OCLC:

763156939