MATS4120 Geometry of geodesics (5 cr)

Content

Riemannian manifolds, tangent bundle, geodesic equation, parallel transport, geodesic flow, Jacobi fields, exponential map.

Completion methods

Written exercises and a talk.

Assessment details

Passing requires a sufficient percentage of exercises and a talk.

After completing the course the student will be familiar with:

- Riemannian manifolds and their geodesics
- the geodesic flow and the structure of the tangent bundle
- Jacobi fields and exponential maps

MATS197 Differential geometry (or other basics of differential
geometry) and knowledge of Riemannian geometry are very useful but not strictly necessary. Multivariate calculus is required.

Lee: Introduction to Riemannian Manifolds,
Paternain: Geodesic Flows