bundles, connections, metrics and curvature Taubes, Clifford 1954- creator text bibliography enk Oxford New York Oxford University Press c2011 2011 monographic eng

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xiii, 298 p. : ill. ; 24 cm. 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. 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. Clifford Henry Taubes. Includes bibliographical references and index. Geometry, Differential QA641 .T238 2011 516.36 9780199605880 (hbk.) 0199605882 (hbk.) 9780199605873 pbk.) 0199605874 (pbk.) 2011499898 SINUS 120106 20150410144038.0 17108854