00478 - Advanced Geometry

Academic Year 2009/2010

  • 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