Uniformisation de l'espace des feuilles de certains feuilletages de codimension un.

This paper deals with codimension one (may be singular) foliations on compact Kälher manifoldswhose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of leaves with a metric of constant non positive curvature wich may degenerate on a 'rigidly' embedded invariant hypersurface. [ABSTRACT FROM AUTHOR]