Lecture Course: Riemannian Geometry

Lecturer: Christian Bär

This is an advanced lecture course on Riemannian geometry. It is a continuation of the introduction to differential geometry. Basic concepts such as manifolds, geodesics, curvature, etc. are now put to use. What can we say about the global shape of spaces with certain curvature properties? Roughly speaking, positive curvature forces a space to close up - it must be compact and its fundamental group finite. Negative curvature, on the other hand, causes geodesics to diverge sharply - the fundamental group of the space can be infinite and very complicated. In fact, the validity and exact formulation of these statements depends on which notion of curvature one uses (sectional curvature, Ricci curvature, or scalar curvature). We want to understand all this. Besides the classical results, some results of current research will be discussed, if time permits. Building on the lecture course, Master's theses can be assigned.

The lectures will be given in English.

When and where:
Lecture course Mondays 16:00-17:30 and Thursdays 12:30-14:00 in house 9, room 0.14
Tutorial class Thursdays 14:15-15:45 in house 9, room 1.10

All further information can be found at this moodle. If interested, please sign up without obligation.