Feuilletages holomorphes admettant une mesure transverse invariante

Abstract

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

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