Differential Geometry

Course content

Curves in R3: Frenet formulas and Fundamental Theorem. Regular surfaces. Inverse image of regular values. Differentiable functions on surfaces. Tangent plane; the differential of a map, vector fields, the first fundamental form. Gauss map, second fundamental form, normal, principal curvatures, principal and asymptotic directions. Gauss map in local coordinates. Covariant derivative, geodesics.