This information sheet indicates how the course will be organized at pandemic code level yellow and green.
If the colour codes change during the academic year to orange or red, modifications are possible, for example to the teaching and evaluation methods.

Differential geometry

Course Code :1001WETDIM
Study domain:Mathematics
Academic year:2020-2021
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
Sandor Hajdu

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.