Applicable differential geometry
M. Crampin, F. A. E. Pirani.
Cambridge : Cambridge University Press, 1986.
394 págs. : ilustraciones ; 23 cm.
Serie: London Mathematical Society lecture note series ; 59
ISBN: 0521231906 (pbk.)
Incluye referencias bibliográficas (p. [383]-385) e índice.
Reseña: MathSciNet, 88i:58001
Contenido
- 0. The background: vector calculus
- 1. Affine spaces
- 2. Curves, functions and derivatives
- 3. Vector fields and flows
- 4. Volumes and subspaces: exterior algebra
- 5. Calculus of forms
- 6. Frobenius's theorem
- 7. Metrics on affine spaces
- 8. Isometries
- 9. Geometry of surfaces
- 10. Manifolds
- 11. Connections
- 12. Lie groups
- 13. The tangent and cotangent bundles
- 14. Fibre bundles
- 15. Connections revisited.