Teachers: Laurent Bessières and Pierre Mounoud
Program:
- Reminder of differential geometry: differential manifolds, tangent bundle, vector fields
- Riemannian metrics: connexions, parallel transport
- Geodesics: local existence and uniqueness, Gauss Lemma, completeness
- Curvatures: Riemann curvatures, Ricci curvature, scalar curvature
- Variational calculus and applications: variation formula for arclenght and energy, Jacobi fields
- Introduction to hyperbolic geometry
Prerequisites:
Differential Geometry.
References:
- J. Cheeger, D. Ebin: Comparison theorems in Riemann Geometry (1975)
- M. Do Carmo: Riemannian Geometry (1992)
- S.Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry (1993)