Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Riemannian manifolds, Model spaces of Riemannian geometry,
Connections, Christoffel symbols, Covariant derivatives, Geodesics,
Existence and uniqueness of geodesics.
- Parallel translations, Riemannian connections, Exponential maps,
Normal coordinates, Geodesics of the model spaces.
- Geodesics and minimizing curves, First variation formula, Gauss lemma,
Hopf-Rinow theorem.
- Riemannian curvature tensor, Symmetries of curvature tensor,
Riemannian submanifolds, Second fundamental form.
- Gauss-Bonnet theorem (local and global form), Jacobi fields, Second
variation formula, Curvature and topology.
- John M. Lee, Riemannian Manifolds; An introduction to
curvature, GTM-176, Springer (1997).
- J. A. Thorpe, Elementary topics in Differential Geometry, UTM,
Springer (1979).
- Marcel Berger, A Panoramic view of Differential Geometry,
Springer (2002).
- Issac Chavel, Riemannian Geometry; A modern introduction,
Cambridge University Press, Cambridge (1993).
- M. P. do Carmo, Riemannian Geometry, Birkhauser, Boatan (1992).
- S. Gallot, D. Hulin, J. Lafontiane, Riemannian Geometry,
Springer-Verlag (1987).
- Peter Petersen, Riemannian Geometry, Springer-Verlag (1998).
