Lecturer(s)


Mikeš Josef, prof. RNDr. DrSc.

Course content

Affine connection, parallel transport, geodesic curves, curvature, torsion, covariant derivative, metrics, Riemann tensor, spaces of constant curvature, special coordinates, variational theory of geodesics, analysis on manifolds with (pseudo)Riemannian metric, the GaussBonnet formula, the Laplacian, harmonic mappings, isometries, conformal mappings.

Learning activities and teaching methods

Work with Text (with Book, Textbook)

Learning outcomes

Sumarize knowledge the classical geometry on manifolds.
1. Knowledge Describe differential properties of manifolds.

Prerequisites

Knowledge the principles on university mathematics level.

Assessment methods and criteria

Oral exam, Written exam
Oral exam.

Recommended literature


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

Eisenhart L.P. (1947). Riemannian Geometry. AMX Princeton.

Gromoll D.,Klingenberg W.,Meyer W. (1968). Riemannsche Geometrie im Grossen. Springer.

Chern S.S., Chen W.H.,Lam K.S. (2000). Lectures on Differential Geometry. World Scientific.

Jost J. (2002). Riemannian Geometry and Geometric Analysis. Springer.
