MATS4120 Geometry of geodesics (5 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

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


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

Description of prerequisites

The knowledge of differential geometry and Riemannian geometry are very useful but not strictly necessary. Multivariate analysis (Vector analysis 1 and 2) is required.

Study materials

Lee: Introduction to Riemannian Manifolds,
Paternain: Geodesic Flows

Completion methods

Method 1

Description:
Lectures and written exercises
Evaluation criteria:
Passing requires a sufficient percentage of exercises.
Select all marked parts
Parts of the completion methods
x

Participation in teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
No published teaching