内容

目次

Preface; Part I. Manifolds, Tensors and Exterior Forms: 1. Manifolds andvector fields; 2. Tensors and exterior forms; 3. Integration of differentialforms; 4. The Lie derivative; 5. The Poincare lemma and potentials; 6.Holonomic and non-holonomic constraints; Part II. Geometry and Topology: 7.R3 and Minkowski space; 8. The geometry of surfaces in R3; 9. Covariantdifferentiation and curvature; 10. Geodesics; 11. Relativity, tensors, andcurvature; 12. Curvature and topology: Synge's theorem; 13. Betti numbers andde Rham's theorem; 14. Harmonic forms; Part III. Lie Groups, Bundles andChern Forms: 15. Lie groups; 16. Vector bundles in geometry and physics; 17.Fiber bundles, Gauss-Bonnet, and topological quantization; 18. Connectionsand associated bundles; 19. The Dirac equation; 20. Yang-Mills fields; 21.Betti numbers and covering spaces; 22. Chern forms and homotopy groups;Appendix A. Forms in continuum mechanics; Appendix B. Harmonic chains andKirchhoff's circuit laws; Appendix C. Symmetries, quarks, and meson masses;Appendix D. Representations and hyperelastic bodies; Appendix E: Orbits andMorse-Bott theory in compact Lie groups.