Course: Differential Geometry I

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Course title Differential Geometry I
Course code MU/03038
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
  • VOJČÁK Petr, RNDr. Ph.D.
Course content
- Smooth manifolds (definition, coordinate systems, atlases, submanifolds, examples of manifolds, mappings of manifolds) - Tangent and cotangent space to the manifold and their relationship (definitions and properties, tangent vectors of curves, tangential views, and kotečný tangent bundles) - Vector fields on manifolds and their properties (different definitions of a vector field and their relations, the Lie bracket and its properties, F-related vector fields and their properties, one-parameter groups, flows and integral curves and their relations) - Differential forms on manifolds and their properties (definition of differential forms; pullback, the exterior product, Lie derivative, exterior derivative, contraction and their relations and properties)

Learning activities and teaching methods
unspecified
Recommended literature
  • C. Isham. Modern Differential Geometry for Physicists. Singapore, 1999.
  • D. Krupka. Matematické základy OTR.
  • J. Musilová, D. Krupka. Integrální počet na Euklidových prostorech a diferencovatelných varietách. SPN, Praha, 1982.
  • John M. Lee. Introduction to Smooth Manifolds. 2006.
  • M. Fecko. Diferenciálna geometria a Lieove grupy pre fyzikov. Bratislava, Iris, 2004.
  • M. Spivak . Calculus on Manifolds. 1965.
  • M. Wisser. Math 464: Notes on Differential Geometry. 2004.
  • O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995.
  • S. Caroll. Lecture Notes on General Relativity.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 5 Winter
Mathematical Institute in Opava Applied Mathematics (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Applied Mathematics (2014-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 1 Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 2 Winter
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Winter