96757 - Riemmannian Geometry

Academic Year 2023/2024

  • 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





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