Differential geometry
Subtitle: bundles, connections, metrics and curvature
By: Clifford Henry Taubes
Series: Oxford graduate texts in mathematics -- 23
Publisher: Oxford University Press
Published: 2011
Place of publication: Oxford ; New York
Language: eng
Number of pages: 298
ISBN-13: 9780199605880; 9780199605873
Subjects: Differential Geometry
Notes: Includes bibliographical references and index.
Table of contents: title: 1. Smooth manifolds; title: 2. Matrices and lie groups; title: 3. Introduction to vector bundles; title: 4. Algebra of vector bundles; title: 5. Maps and vector bundles; title: 6. Vector bundles with C[superscript n] as fiber; title: 7. Metrics on vector bundles; title: 8. Geodesics; title: 9. Properties of geodesics; title: 10. Principal bundles; title: 11. Covariant derivatives and connections; title: 12. Covariant derivatives, connections and curvature; title: 13. Flat connections and holonomy; title: 14. Curvature polynomials and characteristic classes; title: 15. Covariant derivatives and metrics; title: 16. The Riemann curvature tensor; title: 17. Complex manifolds; title: 18. Holomorphic submanifolds, holomorphic sections and curvature; title: 19. The Hodge star.