Course: The Classical Geometry of Manifolds with Metric Fields and Affine Connections

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Course title The Classical Geometry of Manifolds with Metric Fields and Affine Connections
Course code KAG/PGSKG
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 0
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
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 Gauss-Bonnet 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). Non-Riemannian 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.


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