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Lecturer(s)
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Mikeš Josef, prof. RNDr. DrSc.
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Peška Patrik, RNDr. Ph.D.
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Course content
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1. n-dimensional 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.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand theory of Riemannian spaces.
2. Comprehension Explain the conception of the Riemannian geometry
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Prerequisites
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Principles of the analytical geometry.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation.
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Recommended literature
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Conlon L. (1993). Differentiable manifolds: a first course. Boston, Basel, Berlin, Birkhauser.
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Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. VUT Brno.
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Eisenhart, L.P. (2000). Non-Riemannian Geometry. Amer. Math. Soc. Colloquium Publ. 8.
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Gromol D. Klingenberg V., Meyer V. (1980). Riemannova geometrija v celom. Nauka Moskva.
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J. Mikeš at al. (2015). Differential geometry of special mappings. Olomouc.
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Kowalski, O. (1995). Úvod do Riemannovy geometrie. Praha.
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Oprea, J. (2007). Differential geometry and its aplications. MAA Pearson Educ.
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Pogorelov, A. V. (1969). Diferencialnaja geometrija.. Nauka Moskva.
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Poznyak, E. G., Shikin, E. V. (1990). Differential geometry. The first acquaintance (Russian). Izdatel'stvo Moskovskogo Universiteta Moskva.
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Sinyukov, N. S. (1979). Geodesic mappings of Riemannian spaces. Nauka Moskva.
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