Course: Riemannian Geometry

« Back
Course title Riemannian Geometry
Course code KAG/PGSRG
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 15
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Mikeš Josef, prof. RNDr. DrSc.
  • Vanžurová Alena, doc. RNDr. CSc.
Course content
Riemannian and pseudo-Riemannian metric, Christoffel symbols, Riemannian and Ricci tensor. The theory of curvature of Riemannian spaces, special coordinate systems. Geodesic curves. Isometric conformal mappings.

Learning activities and teaching methods
Work with Text (with Book, Textbook)
Learning outcomes
Comprehension of spaces equipped with the metric tensor which are generalization of Euclidean space and have physical applications.
2. Comprehension Recall properties of Riemannian and Ricci tensor of a Riemannian manifold.
Knowledge the principles on university mathematics level.

Assessment methods and criteria
Oral exam

Oral exam.
Recommended literature
  • Eisenhart L.P. (1947). Riemannian Geometry. AMX Princeton.
  • Jost J. (2002). Riemannian Geometry and Geometric Analysis. Springer.
  • Kowalski, O. (1995). Úvod do Riemannovy geometrie. Praha.
  • Mikeš, J., Kiosak, V., Vanžurová, A. (2008). Geodesics Mappings of Manifolds with Affine Connection. Olomouc, Palackého univerzita.
  • Sinyukov, N. S. (1979). Geodesic mappings of Riemannian spaces. Nauka Moskva.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester