M7110 Differential Geometry

Faculty of Science
Spring 2021
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:
M7110/01: Mon 1. 3. to Fri 14. 5. Wed 12:00–13:50 online_M2, K. Neusser
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
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
The course is also listed under the following terms Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2003, Autumn 2006, Autumn 2008, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Spring 2023.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2021/M7110