Stefano PIGOLA


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
  • 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)

  • 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