PřF:M7110 Differential Geometry - Course Information
M7110 Differential GeometryFaculty of Science
- Extent and Intensity
- 2/2/0. 6 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
- Mag. Katharina Neusser, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
- Mon 1. 3. to Fri 14. 5. Tue 12:00–13:50 online_M2
- Timetable of Seminar Groups:
- Global Analysis: differential and integral calculus on manifolds and the basics about Riemannian geometry
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Course objectives
- The course builds on and can be seen as a continuation of the course M7300 Global Analysis. The contents of the course comprise the theory of Lie groups and Lie algebras, homogeneous spaces, the notions of various types of fiber bundles, in particular vector and principal bundles, and the concepts of various types of connections such a linear, principal and Cartan connections.
- Learning outcomes
- After completion of the course a student should have a solid and comprehensive knowledge about the theory of Lie groups and Lie algebras, and the theory of bundles and connections.
- •Lie groups and Lie algebras
- •Homogeneous spaces and Klein geometries
- •Fiber bundles: vector bundles, principal bundles and associated bundles
- •Linear and principal connections on vector respectively principal bundles
- •Geometric structures determining (classes of) distinct connections
- • Holonomy groups
- • Cartan geometries
- Teaching methods
- Lectures, class discussions and assignments
- Assessment methods
- Exam, assignments
- Language of instruction
- Further comments (probably available only in Czech)
- Study Materials
The course is taught once in two years.
- Teacher's information
- Enrolment Statistics (Spring 2021, recent)
- Permalink: https://is.muni.cz/course/sci/spring2021/M7110