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:
2023-2024
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 calculus 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:
Pass - fail
Language:
English, Finnish