## Chern connections in the context of CR-geometry

### 1.Preliminaries: Chern theorem

This post is a result of several discussions with Rodiohn Déev.

Fix a complex manifold and a complex vector bundle over .

Recall that a structure of holomorphic bundle on is given by an operator

which satisfies -Leibniz identity

and the integrability condition

For the reader who is more accustomed …