MATS1980 Riemannian geometry (4 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024
Description
The course is an introduction to Riemannian geometry. Riemannian manifolds: Riemannian metric, geodesics, exponential mapping, isometries, curvature etc
Learning outcomes
After passing the course successfully the student
- knows the meaning of the metric in Riemannian geometry
- can describe geodesics in simple cases
- knows the connection between geodesics and the exponential map
- can recognize different isometric versions of Riemannian manifolds
- knows the basic properties of Riemannian curvature tensor
Description of prerequisites
MATS1960 Introduction to manifolds
Literature
- John M. Lee: Riemannian manifolds. An introduction to curvature. Graduate Texts in Mathematics 176, Springer, 1997. ISBN 0-387-98322-8
Completion methods
Method 1
Evaluation criteria:
Course exam and exercises
Select all marked parts
Method 2
Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x
Participation in teaching (4 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
x
Exam (4 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish