SubjectsSubjects(version: 942)
Course, academic year 2023/2024
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Riemannian Geometry 2 - NMAG566
Title: Riemannova geometrie 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Roman Golovko, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Volitelné
Classification: Mathematics > Geometry
Incompatibility : NGEM036
Pre-requisite : NMAG411
Interchangeability : NGEM036
Is interchangeable with: NGEM036
Annotation -
Last update: prof. RNDr. Oldřich Kowalski, DrSc. (10.09.2013)
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: T_MUUK (16.05.2013)

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

doctoral students.

Course completion requirements -
Last update: Roman Golovko, Ph.D. (30.04.2020)

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.

Literature -
Last update: T_MUUK (16.05.2013)

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: doc. RNDr. Svatopluk Krýsl, Ph.D. (25.02.2019)

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

Requirements to the exam -
Last update: doc. RNDr. Svatopluk Krýsl, Ph.D. (25.02.2019)

The exam is oral with a written preparation.

The exam consists of testing of definition, theorems and their applications.

Syllabus -
Last update: Mgr. Tomáš Salač, Ph.D. (18.02.2021)

Gradient, divergence, Laplace operator and its spectrum, harmonic functions and forms, homogeneous Riemannian spaces, other topics can be chosen to meet interests of students.

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