Elementary topics in differential geometry
John A. Thorpe.
New York : Springer-Verlag, ©1979.
xiii, 253 págs. : ilustraciones ; 24 cm.
Serie: Undergraduate texts in mathematics
ISBN: 0387903577 (USA), 3540903577 (Alemania)
Incluye índices y bibliografía: p. 245.
Reseña: MathSciNet, 80e:53001
Contenido
- 1. Graphs and level sets
- 2. Vector fields
- 3. The tangent space
- 4. Surfaces
- 5. Vector fields on surfaces; orientation
- 6. The Gauss map
- 7. Geodesics
- 8. Parallel transport
- 9. The Weingarten map
- 10. Curvature of plane curves
- 11. Arc length and line integrals
- 12. Curvature of surfaces
- 13. Convex surfaces
- 14. Parametrized surfaces
- 15. Local equivalence of surfaces and parametrized surfaces
- 16. Focal points
- 17. Surface area and volume
- 18. Minimal surfaces
- 19. The exponential map
- 20. Surfaces with boundary
- 21. The Gauss-Bonnet theorem
- 22. Rigid motions and congruence
- 23. Isometries
- 24. Riemannian metrics.