96757 - RIEMANNIAN GEOMETRY

Scheda insegnamento

Anno Accademico 2021/2022

Conoscenze e abilità da conseguire

At the end of the course, the student acquires advanced knowledge on differential calculus on smooth manifolds and knowledge on the main problems and methods that arise from the study of Riemannian structures, particularly with regard to geodesics. The student knows the fundamental examples and is able to handle the main tools of the theory that can be used to construct mathematical models.

Contenuti

1) topological manifold

2)smooth structures

3) vector fields, differential forms, tensor bundle

4) metric

5) connections

6) curvautres

Testi/Bibliografia

J.M. Lee: introduction to smooth manifolds

Do Carmo: Riemannian geometry

Metodi didattici

black board presentation

Modalità di verifica e valutazione dell'apprendimento

take home exam+ oral interview

Orario di ricevimento

Consulta il sito web di Emanuele Latini