Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Geometry

Code

fedifg1u0um17em

Title

Topics in differential geometry (l)

Usual semester

Autumn

Published semester

2025/26/2

ECTS

3

Language

hu

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyze mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

Characterization of convex surfaces in differential geometry. The Steiner–Minkowski formula, Herglotz’s integral formula, rigidity theorems for convex surfaces. Ruled surfaces and line congruences. Surfaces of constant curvature. Chebyshev nets, the sine–Gordon equation, Bäcklund transformation, Hilbert’s theorem. Comparison theorems. Variational problems in differential geometry. The Euler–Lagrange equation, the brachistochrone problem, geodesics, Jacobi fields, Lagrangian mechanics, symmetries and invariants, minimal surfaces, conformal parametrization, harmonic maps. Prerequisite knowledge: rudiments of differential geometry

Assessment method

(written or oral) exam plus term mark

Bibliography

lecture notes

Recommended bibliography

W. Blaschke: Einführung in die Differentialgeometrie, Springer-Verlag 1950. J.A. Thorpe: Elementary Topics in Differential Geometry, Springer-Verlag 1979. J.J. Stoker: Differential Geometry, John Wiley & Sons Canada, Ltd.; 1989. F.W. Warner: Foundations of Differential Manifolds and Lie Groups, Springer-Verlag, 1980.

Programmes of the course