Syllabus: Reminder of basic constructions of Differential Geometry (principal and mean curvature, Gauss curvature, normal and geodesic curvature), covariant derivative and geodesic curves, length functional, Clairaut’s Theorem, local and global Gauss-Bonnet Theorem, surfaces of constant curvature, topological structure of surfaces, Euler characteristic.
Literature: 1) do Carmo M.: Differential Geometry of Curves and Surfaces, 2nd ed. Dover 2016, 2) McCleary J.: Geometry from the Differentiable Point of View, 2nd ed. Cambridge 2012