MU25009 Chapters in Differential Geometry

Mathematical Institute in Opava
Summer 2026
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Hynek Baran, Ph.D. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava
Timetable
Thu 11:25–13:00 R2
  • Timetable of Seminar Groups:
MU25009/01: Tue 13:05–14:40 R2, P. Vojčák
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 course covers parts of classical and modern differential geometry, appropriate for all graduates of mathematics. The course is independent from the basic course of differential geometry.
Syllabus
1. Curves in Euclidean spaces: Frenet frame, Frenet-Serret formulas.
2. Hypersurfaces in Euclidean spaces: the first and second fundamental form, Gauss-Weingarten equations, Gauss-Mainardi-Codazzi equations, principal curvatures, mean and Gaussian curvature, theorema egregium, Gauss map, the third fundamental form.
3. Curves on a surface, parallel transport, geodesics, geodesic and normal curvature, geodesic and normal torsion. Special parameterizations and nets (hlavní, asymptotická, geodetická, Čebyševova, their applications).
4. Minimal surfaces, pseudospheric surfaces, models of Lobachevsky geometry.
Literature
    required literature
  • M. Marvan. Geometrie nelineárních útvarů. URL info
    recommended literature
  • V.A. Toponogov. Differential geometry of curves and surfaces : a concise guide. Boston, 2006. info
  • M.P. do Carmo. Differential geometry of curves and surfaces. 1976. ISBN 0-13-212589-7. info
    not specified
  • S. P. Novikov, I. A. Taimanov. Modern Geometric Structures and Fields. Amer. Math. Soc., 2006. 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
The course comprises lectures and tutorials. To pass the course, the first step is to earn credit for tutorials (by earning 70% on a written test). The final exam, which consists of a written and on oral part, tests theoretical knowledge and understanding of the subject, including proofs.
The course is also listed under the following terms Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2026/MU25009