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Lecturer(s)
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Mikeš Josef, prof. RNDr. DrSc.
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Course content
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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.
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Learning activities and teaching methods
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Work with Text (with Book, Textbook)
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Learning outcomes
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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.
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Prerequisites
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Knowledge the principles on university mathematics level.
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Assessment methods and criteria
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Oral exam
Oral exam.
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Recommended literature
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Eisenhart L.P. (1947). Riemannian Geometry. AMX Princeton.
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Jost J. (2002). Riemannian Geometry and Geometric Analysis. Springer.
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Kowalski, O. (1995). Úvod do Riemannovy geometrie. Praha.
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Mikeš, J., Kiosak, V., Vanžurová, A. (2008). Geodesics Mappings of Manifolds with Affine Connection. Olomouc, Palackého univerzita.
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Sinyukov, N. S. (1979). Geodesic mappings of Riemannian spaces. Nauka Moskva.
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