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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: T_MUUK (20.05.2004)
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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: KOWALSKI/MFF.CUNI.CZ (28.03.2008)
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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: KOWALSKI/MFF.CUNI.CZ (28.03.2008)
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The methods of teaching is a standard lecture and exercise sessions. The topic can be studied individually, as well. Last update: KOWALSKI/MFF.CUNI.CZ (28.03.2008)
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Gradient, Divergence and Laplacian on a Riemannian manifold, Harmonic functions, Hopf Lemma and Spectrum of the Laplacian on compact Riemannian manifolds, Homogeneous Riemannian manifolds, Symmetric spaces. Last update: T_MUUK (05.05.2004)
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