Frankel, Theodore, 1929-
The geometry of physics : an introduction / Theodore Frankel.
— Rev. ed. — Cambridge : Cambridge University Press, 2001, c1997. xxiv, 666 p. : il. ; 26 cm.
Contiene correcciones a la ed. de 1997, y un nuevo apéndice.
Incluye referencias bibliográficas (p. 651-653) e índice.
Contenido: Part 1. Manifolds, tensors and exterior forms: 1. Manifolds and vector fields — 2. Tensors and exterior forms — 3. Integration of differential forms — 4. The Lie derivative — 5. The Poincaré lemma and potentials — 6. Holonomic and nonholonomic constraints.
Contenido: Part 2. Geometry and topology: 7. $R3$ and Minkowski space — 8. The geometry of surfaces in $R3$ — 9. Covariant differentiation and curvature — 10. Geodesics — 11. Relativity, tensors, and curvature — 12. Curvature and topology: Synge's theorem — 13. Betti numbers and de Rham's theorem — 14. Harmonic forms.
Contenido: Part 3. Lie groups, bundles and Chern forms: 15. Lie groups — 16. Vector bundles in geometry and physics — 17. Fiber bundles, Gauss-Bonnet, and topological quantization — 18. Connections and associated bundles — 19. The Dirac equation — 20. Yang-Mills fields — 21. Betti numbers and covering spaces — 22. Chern forms and homotopy groups.
Contenido: Appendix A. Forms in continuum mechanics — Appendix B. Harmonic chains and Kirchhoff's circuit laws.
ISBN 0521387531 (pbk). — ISBN 052138334X
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