MU25021 Supplementary Tutorial in Differential Geometry I

Mathematical Institute in Opava
Winter 2024

The course is not taught in Winter 2024

Extent and Intensity
0/2/0. 4 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Jiřina Jahnová, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jiřina Jahnová, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA(N)
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The goal of the course is a detailed analysis of hands-on approaches to the subject matter presented in the lectures on Differential Geometry I and clarifying less trivial aspects thereof for improving knowledge and skills of students with emphasis on their individual work. Solving certain problems may involve the use of computer algebra software (Maple).
Syllabus
  • Smooth manifolds: implicit versus parametrical description of smooth manifolds, examples; embedding and immersion, examples; blow-up, connected sum and some less known examples of manifolds; Riemann surfaces as an introduction to complex differential geometry.
    Tangent and cotangent bundle: vector fields, flows, integral curves, Lie derivative of functions and vector fields, examples; Frobenius theorem and its applications; differential forms and operations on them, examples; exterior differential systems, examples.
Literature
    required literature
  • J. Lafontaine. An Introduction to Differential Manifolds. 2015. info
  • L. Tu. An Introduction to Manifolds. 2014. info
  • P. M. Gadea, J. M. Masqué, I. V. Mykytyuk. Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers. 2013. info
  • S. K. Donaldson. Riemann Surfaces. 2011. info
    recommended literature
  • M. Spivak. A Comprehensive Introduction to Differential Geometry I. 1999. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
To get course credits it is neccessary to solve three projects assigned by the instructor.
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