Subjects

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Differential Geometry - NMTM301

Title:	Diferenciální geometrie
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Annotation -

Last update: RNDr. Jakub Staněk, Ph.D. (14.06.2019)

Basic course of classical differential geometry curves and surfaces.

Course completion requirements -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (01.10.2021)

It is necessary to successfully solve two sets of homeworks that will be assigned during the term.

Literature -

Last update: RNDr. Jakub Staněk, Ph.D. (14.06.2019)

K. Tapp: Differential Geometry of Curves and Surfaces, Springer, 2016

F. Borceux: A Differential Approach to Geometry (Geometric Trilogy III), Springer, 2014

A. Pressley: Elementary Differential Geometry, Springer, 2010

Requirements to the exam -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (01.10.2021)

A written exam following the syllabus of the subject in the scope of the lecture.

Syllabus -

Last update: doc. RNDr. Antonín Slavík, Ph.D. (01.10.2021)

Plane and space curves, examples. Arclenght parametrization, Frenet frame, Frenet formulas, curvature and torsion, evolutes and involutes.

Parametrized surfaces, examples. Curves on surfaces. First fundamental form and its applications. Surface mapping (isometries, conformal mappings). Normal curvatures and second fundamental form. Principal directions and principal curvatures. Mean and Gaussian curvature, Theorema egregium, geodesic curves.