This course shall deal with Riemannian geometry in the large. It shall be a continuation of Differential Geometry I and also serve as preparation for modern developments in geometric analysis and mathematical physics. Its content shall be a selection of the following topics:
- basic notions of differential topology
- geodesics, the exponential mapping and the Hopf-Rinow theorem
- comparison theorems and connections between curvature and topology
- differential forms, Stokes' theorem and de Rham cohomology
- spaces of constant curvature, Lie groups and homogeneous spaces
- isometries, Killing fields and the Myers-Steenrod theorem
Literature: to be announced.