Differential Geometry

Differential geometry is about curved manifolds. The course gives an introduction to curves and surfaces in two- and three-dimensional space.

The central concept is curvature. In the geometry of curved surfaces, geodesics play the role of straight lines in the plane as the locally shortest way between two points. At the end, we treat the Gauss-Bonnet theorem, which connects the integral of the curvature with the topological properties of the surface.

The course is given every other year, in the spring semester in odd-numbered years.