Differential Geometry II

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
Program of Studies:
Undergraduate Studies
Semester: H
Hours per week (Lec/Tut/L): 2/2/0
Code: PM333
Course type: Elective
Compulsory course
for the specialization "Pure Mathematics"
Erasmus students: Yes