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Differential geometry 1

Code: 92898
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Zvonko Iljazović
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
The aim of the Course is to develope the geometry of n-dimensional oriented surfaces in R(n+1). By viewing such surfaces as level sets of smooth functions, the global ideas can be introduced early without the need for preliminary development of sophisticated machinery. The calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential 1-forms are introduced only as needed for use in integration.

1. What is differential geometry?
2. Graphs and Level Sets.
3. Vector Fields. The Tangent Space.
4. Surfaces. Vector Fields on Surfaces. Lagrange multiplier.
5. Orientation. The Gauss Map
6. Geodesics.
7. Parallel Transport. Covariant Derivative.
8. The Weingarten Map.
9. Normal Curvature .
10. Curvature of Plane Curves. Frenet-Serret Formulas.
11. Arc Length and Global Parametrization.
12. Differential 1-forms and Line Integrals.
13. Gauss-Kronecker Curvature. Mean Curvature.
14. The Second Fundamental Form.
15. Convex Surfaces. Elements of Critical Point Theory.
1. semester
Mandatory course - Regular study - Theoretical Mathematics
Consultations schedule: