Differential Geometry II
Description
Proof of Theorema Egregium, charts and local coordinate systems (atlas), smooth maps between surfaces, differential of a smooth map, normal and geodesic curvature, Meusnier’s theorem, vector fields on surfaces, covariant derivative of vector fields, parallel transport, Christoffel symbols, Hilbert’s theorem, Liebmann’s theorem, geodesics, minimal surfaces, Gauss-Bonnet theorem (local-global version and applications).
Division: Pure Mathematics