- Docente: Emanuele Latini
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
Learning outcomes
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.
Course contents
1) topological manifold
2)smooth structures
3) vector fields, differential forms, tensor bundle
4) metric
5) connections
6) curvautres
Readings/Bibliography
J.M. Lee: introduction to smooth manifolds
D Carmo: Riemannian geometry
Teaching methods
black board presentation
Assessment methods
take home exam+ oral interview
Office hours
See the website of Emanuele Latini