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Course, academic year 2023/2024
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Fundamentals of Riemannian Geometry 2 - NGEM036
Title: Základy Riemannovy geometrie 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Oldřich Kowalski, DrSc.
Classification: Mathematics > Geometry
Pre-requisite : NGEM011
Interchangeability : NMAG566
Is incompatible with: NMAG566
Is interchangeable with: NMAG566
Annotation -
Last update: T_MUUK (20.05.2004)
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.
Aim of the course -
Last update: KOWALSKI/MFF.CUNI.CZ (28.03.2008)

The goal of this topic is an advanced course in Riemannian Geometry, which is especially suitable for the potential

doctoral students.

Literature -
Last update: KOWALSKI/MFF.CUNI.CZ (28.03.2008)

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.

Teaching methods -
Last update: KOWALSKI/MFF.CUNI.CZ (28.03.2008)

The methods of teaching is a standard lecture and exercise sessions. The topic can be studied individually, as well.

Syllabus -
Last update: T_MUUK (05.05.2004)

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.

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