Structure des feuilletages kähleriens en courbure semi-négative

Abstract

This paper is concerned with (tranversely) Kähler foliations. We proved that the lie algebra associated to the holonomy pseudogroup is semisimple under some negativity conditions for the transverse Ricci tensor. This result can be interpreted as a foliated analogue of a theorem due to Nadel concerning the automorphism group of the universal covering of certain compact complex manifolds. As an application of our methods, we also show that the leaves of holomorphic foliations with trivial canonical class are closed submanifolds.