#
PřF:M7110 Differential Geometry - Course Information

## M7110 Differential Geometry

**Faculty of Science**

Autumn 2016

**Extent and Intensity**- 2/2. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
**Teacher(s)**- doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
**Guaranteed by**- doc. RNDr. Martin Čadek, CSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 19. 9. to Sun 18. 12. Mon 12:00–13:50 M4,01024
- Timetable of Seminar Groups:

*J. Šilhan* **Prerequisites**-
**M5130**Global Analysis

Before enrolling the course the students should pass "Differential Geometry of Curves and Surfaces" and "Global Analysis". **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 presents the basic knowledge of contemporary differential
geometry that prepares the student for independent reading of mathematical literature.

At the end of the course students should be able to:

*explain the connection between Lie groups and their Lie algebras

*derive the Lie bracket of the classical (and also not so classical) Lie groups

*understand the relationship between the principal and associated bundles and connections on them

*understand the relationship between different forms of connection and their impact on the geometry of a Riemannian space **Syllabus**- Lie groups and Lie algebras. Actions of Lie groups on manifolds. Vector bundles and fibered manifolds. Principal and associated bundles. Connections on principal bundles, parallel transport. Linear connections on vector bundles. Koszul's approach to connections on tangent bundles. Riemannian metric and the Levi-Civita connection. Some applications.

**Literature**- KOLÁŘ, Ivan, Jan SLOVÁK and Peter W. MICHOR.
*Natural Operations in Differential Geometry*. Berlin-Heidelberg-New York: Springer-Verlag, 1993. 434 pp. ISBN 3-540-56235-4. info - Sharpe, Richard W. Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Springer, 1997

- KOLÁŘ, Ivan, Jan SLOVÁK and Peter W. MICHOR.
**Teaching methods**- Lectures and tutorials.
**Assessment methods**- An oral exam.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course is taught once in two years.

General note: podzim 2006 jako konzultovaná četba.

- Enrolment Statistics (Autumn 2016, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2016/M7110