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This paper deals with codimension one (may be singular) foliations on compactK\"alher manifolds whose conormal bundle is assumed to be pseudo-effective.Using currents with minimal singularities, we show that one can endow the spaceof leaves with a metric of constant non positive curvature wich may degenerateon a rigidly embedded invariant hypersurface.

Uniformisation de l'espace des feuilles de certains feuilletages de codimension 1