Advanced Geometry A

An introduction to Riemannian Geometry

This is a traditional course in basic Riemannian geometry. Starting from the notion of Riemannian metric and corresponding covariant differentiation, we shall present the metric space structure of a Riemannian manifold related to the theory of geodesics and the link between the sign of the (Riemann or Ricci) curvature tensors and the topology of the underlying space

__Useful links__

Textbooks

An introduction to Riemannian Geometry

This is a traditional course in basic Riemannian geometry. Starting from the notion of Riemannian metric and corresponding covariant differentiation, we shall present the metric space structure of a Riemannian manifold related to the theory of geodesics and the link between the sign of the (Riemann or Ricci) curvature tensors and the topology of the underlying space

- G.F.B.
Riemann,
*On the Hypotheses which lie at the Bases of Geometry*(url) - M.
Gromov,
*Sign and Geometric Meaning of Curvature.*Rend. Sem. Mat. Fis. Milano**61**(1991), 9-123. (url)

Textbooks

- M.P. Do Carmo, Riemannian Geometry. Birkhäuser Boston, Inc., Boston, MA, 1992.
- J.M Lee, Riemannian Manifolds: an introduction to curvature. Graduate Texts in Mathematics, 176. Springer-Verlag, New York, 1997.

Monday, 10am - 1pm, Room 2.1 (Via Castelnuovo)

Thursday, 10am - 1pm, Room 4.1 (Via Castelnuovo)

last updated 2017/12/16