Courses

Proof of the Marvelous Theorem, maps and local coordinate systems on surfaces (atlas), differentiable mappings between surfaces, differential of differentiable mapping, perpendicular and geodesic curvature, Meusnier's theorem, vector fields on surfaces, invariant derivative of a field along a curve on a surface, parallel transport, Christoffel symbols, Hilbert's theorem, Liebmann's theorem, geodesic curves, surfaces of minimal area, the Gauss-Bonnet theorem (global-local version and applications).