Feuilletages holomorphes admettant une mesure transverse invariante

Let $\mathcal{F}$ be a regular codimension 1 holomorphic foliation on a compact K" ahler manifold. One assumes in addition that $\mathcal{F}$ possesses a transverse invariant positive current. The aim of this paper is to establish the following alternative: - There exists an invariant hypersurface. - The foliation admits a transverse invariant hermitian metric with constant curvature