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In Part 2 the knowledge about Riemannian geometry is extended, e.g.,by the following topics: Gradient, Divergence, Laplacian, Harmonic functions, Hopf Lemma, Spectrum of the Laplacian, Homogeneous Riemannian manifolds, Symmetric spaces.
Last update: Kowalski Oldřich, prof. RNDr., DrSc. (10.09.2013)
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The goal of this topic is an advanced course in Riemannian Geometry, which is especially suitable for the potential doctoral students. Last update: T_MUUK (16.05.2013)
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There will be several homeworks. As a requirement to take the final exam students must submit solutions to at least one homework. The final exam will be in the form of a distance interview. Last update: Golovko Roman, Ph.D. (30.04.2020)
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S.Kobayashi and K.Nomizu, Foundations of Differential geometry I, II, Interscience Publishers 1963, 1969.
S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic press, 1978.
R.L.Bishop, R.J.Crittenden, Geometry of Manifolds, AMS Chelsea Publishing, 2001.
M. Berger, P. Gauduchon, E. Mazet, Le Spectre d´une Variété Riemannianne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag 1971. Last update: T_MUUK (16.05.2013)
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The methods of teaching is a standard lecture. The topic can be studied individually, as well. Last update: Krýsl Svatopluk, doc. RNDr., Ph.D. (25.02.2019)
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The exam is oral with a written preparation.
The exam consists of testing of definition, theorems and their applications. Last update: Krýsl Svatopluk, doc. RNDr., Ph.D. (25.02.2019)
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Gradient, divergence, Laplace operator and its spectrum, harmonic functions and forms, homogeneous Riemannian spaces, other topics can be chosen to meet interests of students. Last update: Salač Tomáš, Mgr., Ph.D. (18.02.2021)
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