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Lecturer(s)
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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. Geometric objects on manifolds. 3. Tensors on manifolds. 4. Manifolds with affine connection, covariant derivation. 5. Parallel transport. Geodetic curves. 6. Riemannian and Ricci tensors. 7. Riemannian metrics, length of curves. 8. Variation problems on manifolds. 9. Geodetic curves on Riemannian space. 10. Properties of Riemannian and Ricci tensors. 11. Sectional curvature on Riemannian space. 12. Spaces on constant curvature, Einstein spaces. 13. Isometric and conformal mappings.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
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Learning outcomes
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Understand basic topics of differential and integral calculus on manifolds.
1. Knowledge List of the principles of the diferential theory of the curves and surfaces.
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Prerequisites
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unspecified
KAG/ZG2
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Assessment methods and criteria
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Oral exam, Written exam, Student performance
Active participation.
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Recommended literature
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Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. VUT Brno.
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Gray, A. (2006). Modern Differential Geometry of Curves and Surfaces.. Chapman \& Hall/CRC, Boca Raton, FL.
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Kolář I. (2002). Úvod do globální analýzy. MU Brno.
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Kreyszig E. (2013). Differential geometry.. Dover publ.
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Metelka, J. (1969). Diferenciální geometrie. SPN Praha.
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Podolský J. (2006). Teoretická mechanika v jazyce diferenciální geometrie. UK Praha.
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Struik J. D. (1961). Lectures on classical differential geometry. Courier corp.
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Vanžurová, A. (1996). Diferenciální geometrie křivek a ploch. UP Olomouc.
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