MATS4120 Geometry of geodesics (5 cr)

Grading scale

Pass-fail

Teaching languages

Finnish , English

Learning outcomes

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

Study methods

Written exercises and a talk.

Content

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

Materials

Lee: Introduction to Riemannian Manifolds,
Paternain: Geodesic Flows

Assessment criteria

Passing requires a sufficient percentage of exercises and a talk.

Prerequisites

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.