MATS1970 Differential geometry on manifolds (4 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
Differentiable manifolds, tangent bundles, tensor fields, differential forms.
Learning outcomes
After passing the course successfully the student
- can determine the tangent bundle of a given submanifold
- knows the abstract version of concepts such as the tangent bundle and cotangent bundle
- can handle differential forms
Additional information
Lectured biennially. The course is tentatively planned to be taught in the fall semesters of 2025 and 2027.
Description of prerequisites
Introduction to manifolds
Literature
- John M. Lee:Introduction to smooth manifolds. Graduate Texts in Mathematics 218, Springer, 2006. ISBN 978-0-387-95448-6
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