Lecturer(s)


Mikeš Josef, prof. RNDr. DrSc.

Course content

1. ndimensional differentiable manifolds. 2. Tensors on manifolds. 3. Manifolds with affine connection, covariant derivation. 4. Parallel transport. Geodetic curves. 5. Riemannian and Ricci tensors. 6. Riemannian metrics, length of curves. 7. Geodetic curves on Riemannian space. 8. Properties of Riemannian and Ricci tensors. 9. Sectional curvature on Riemannian space. 10. Spaces of constant curvature, Einstein spaces. 11. Isometric and conformal mappings.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)

Learning outcomes

Understand theory of Riemannian spaces.
2. Comprehension Explain the conception of the Riemannian geometry

Prerequisites

Principles of the analytical geometry.

Assessment methods and criteria

Oral exam, Written exam
Credit: active participation.

Recommended literature


Conlon L. (1993). Differentiable manifolds: a first course. Boston, Basel, Berlin, Birkhauser.

Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. VUT Brno.

Eisenhart, L.P. (2000). NonRiemannian Geometry. Amer. Math. Soc. Colloquium Publ. 8.

Gromol D. Klingenberg V., Meyer V. (1980). Riemannova geometrija v celom. Nauka Moskva.

Kowalski, O. (1995). Úvod do Riemannovy geometrie. Praha.

Oprea, J. (2007). Differential geometry and its aplications. MAA Pearson Educ.

Pogorelov, A. V. (1969). Diferencialnaja geometrija.. Nauka Moskva.

Poznyak, E. G., Shikin, E. V. (1990). Differential geometry. The first acquaintance (Russian). Izdatel'stvo Moskovskogo Universiteta Moskva.

Sinyukov, N. S. (1979). Geodesic mappings of Riemannian spaces. Nauka Moskva.
