## Sheaf Theory and Metrics on Fiber Bundles

### Ugo Bruzzo

Contents:

1. An introduction to Riemannian and Kaeherian geometries (reference texts: Kobayashi-Nomizu, Foundations of Differentiable Manifolds Vol I , for the Riemannian Geometry part; Wells, Differential Analysis on Complex Manifolds, for Kaehlerian Geometry).

2. An introduction to sheaves, if needed. Reference texts: my notes; Godement, Theorie des fascieaux.

3. Differential geometric aspects of complex vector bundles. Text: Kobayashi, Differential geometry of complex vector bundles.

4. (for the PhD students) Relation between stability and the existence of special metrics.