M7110 Differential Geometry

Faculty of Science
Autumn 2008
Extent and Intensity
4/2. 6 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. Lukáš Vokřínek, PhD. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Wed 13:00–14:50 MS2,01022, Fri 10:00–11:50 MS2,01022
  • Timetable of Seminar Groups:
M7110/01: Wed 15:00–16:50 MS2,01022, L. Vokřínek
Prerequisites
M5130 Global Analysis
Before enrolling the course the students should go through "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
Course objectives
The course presents the basic knowledge of contemporary differential geometry that prepares the student for independent reading of mathe- matical literature.
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 matric 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
Assessment methods
lectures 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.
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 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Spring 2021.
  • Enrolment Statistics (Autumn 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M7110