Differential geometry

Course Code :1001WETDIM
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)Tom Mestdag
Jens Hemelaer

3. Course contents *

1. Curves

Curves in 3-dimensional Euclidean space. The canonical representation of a curve. The fundamental theorem.

2. Surfaces

Surfaces in 3-dimensional Euclidean space. Tangent plane. The first fundamental form. Isometries. Normal and geodesic curvature. Weingarten map, Gaussian curvature, mean curvature, principal curvatures. Christoffel symbols, geodesic lines, the Gauss-Bonnet formula, Riemann curvature tensor. Theorema Egregium.

3. Riemannian manifolds

Generalities about differential manifolds. Examples: matrix groups and surfaces in R^3. Tangent spaces of a manifold. Riemannian manifolds. Parallel transport and linear connections. The Jacobi equation and the Riemann curvature tensor. Other areas of modern differential geometry.