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Riemannian geometry /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, New Jersey :
Princeton University Press,
1997.
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| Colección: | Princeton landmarks in mathematics and physics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Preface; Contents; CHAPTER I Tensor analysis ; 1. Transformation of coördinates. The summation convention ; 2. Contravariant vectors. Congruences of curves ; 3. Invariants. Covariant vectors ; 4. Tensors. Symmetric and skew-symmetric tensors
- 5. Addition, subtraction and multiplication of tensors. Contraction 6. Conjugate symmetric tensors of the second order. Associate tensors; 7. The Christoffel 3-index symbols and their relations ; 8. Riemann symbols and the Riemaun tensor. The Ricci tensor; 9. Quadratic differential forms ; 10. The equivalence of symmetric quadratic differential forms
- 11. Covariant differentiation with respect to a tensor gij CHAPTER II Introduction of a metric; 12. Definition of a metric. The fundamental tensor ; 13. Angle of two vectors. Orthogonality ; 14. Differential parameters. The normals to a hypersurface ; 15. N-tuply orthogonal systems of hypersurfaces in a Vn
- 16. Metric properties of a space Vn immersed in a Vm 17. Geodesics ; 18. Riemannian, normal and geodesic coördinates; 19. Geodesic form of the linear element. Finite equations of geodesics; 20. Curvature of a curve ; 21. Parallelism ; 22. Parallel displacement and the Riemann tensor ; 23. Fields of parallel vectors
- 24. Associate directions. Parallelism in a sub-space 25. Curvature of Vn at a point ; 26. The Bianchi identity. The theorem of Schur ; 27. Isometric correspondence of spaces of constant curvature. Motions in a Vn ; 28. Conformal spaces. Spaces conformal to a flat space; CHAPTER III Orthogonal ennuples