Riemannian Geometry
A.Y. 2018/2019
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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.
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
Professors:
Mastrolia Paolo, Rigoli Marco
Professor(s)