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

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
No published teaching
x

Exam (4 cr)

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