- Docente: Sergio Venturini
- Credits: 12
- SSD: MAT/03
- Language: Italian
- Moduli: Sergio Venturini (Modulo 1) Stefano Francaviglia (Modulo 2)
- Teaching Mode: In-person learning (entirely or partially) (Modulo 1); In-person learning (entirely or partially) (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Learning outcomes
Basic elements of differential geometry, differentiable manifolds as ringed spaces.
Course contents
Differentiable manifolds: sheaves of continuous functions,
differentiable manifolds, tangent and cotangent bundle.
Differential forms: the exterior derivative, integration of
differential forms and Stokes formula.
Vector fields: Poisson bracket, Jacobi identy, Frobenius
theorem.
Absolute differential calculus: connections on vector bundles,
Levi-Civita connection on Riemannian manifolds
Teaching methods
Front lessons
Assessment methods
Oral examinations
Office hours
See the website of Sergio Venturini
See the website of Stefano Francaviglia