Riemannian Geometry

A.Y. 2018/2019
6
Max ECTS
42
Overall hours
SSD
MAT/03
Language
Italian
Learning objectives
The aim of the course i sto introduce the student to some advanced topic in the classical geometry of surfaces in Euclidean space.
Expected learning outcomes
A working knowledge of the moving frame and of the analytical tools in the study of differential geometry.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
1. The geometry of surfaces
2. Riemann surfaces
3. The moving frame for surfaces in R^3
4. Functions of holomorphic type
5. Enneper-Weierstrass representation
6. Integral formulas and Ros theorem
7. Examples of minimal surfaces in R^3
8. The "genesis" of Bernstein theorem
9. First and second variation of area; stable surfaces.
MAT/03 - GEOMETRY - University credits: 6
Lessons: 42 hours