M6722 Differential Geometry of Surfaces

Faculty of Science
Spring 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Ivan Kolář, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Prerequisites
M5721 Diff. Geom. of curves
The course "Differential Geometry of Curves" should be absolved.
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
A rounded survey on the main methods and results of the differential geometry of surfaces in the euclidean three-space is presented.
Syllabus
  • Surfaces: the first fundamental form, envelops, the second fundamental form, principal curves, ruled surfaces. Inner geometry of surfaces: isometries, parallel transport of vectors on a surface, geodesics, surfaces with constant Gauss curvature.
Literature
  • Doupovec,M. Diferenciální geometrie a tensorový počet. Skriptum FSt VUT Brno,1999.
  • Vanžurová,A. Diferenciální geometrie křivek a ploch. Skriptum PU Olomouc, 1996.
  • Kolář,I. Diferenciální geometrie křivek a ploch. Skriptum v přípravě.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2001, Spring 2002, Spring 2005.
  • Enrolment Statistics (Spring 2003, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2003/M6722