Lecturer

Urs Lang

Coordinator

Stefano Decio

Content

Introduction to Riemannian geometry in combination with some elements of modern metric geometry. Topics covered include: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of Riemannian manifolds.

Prerequisites

Prerequisite is a working knowledge of elementary differential geometry (curves and surfaces in Euclidean space), differentiable manifolds, and differential forms.

Exercises

The new exercises will be posted here on Tuesday. We expect you to look at the problems and to prepare questions for the exercise class on Friday.

Exercise classes

Literature

• M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992
• S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004
• B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press 1983
• S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volume I, Wiley 1963