Holomorphic foliations admitting a transverse invariant measure (Q744947)

The paper is mainly devoted to prove the following result. Let \(F\) be a regular codimension-one holomorphic foliation on a compact Kähler manifold. If one assumes that \(F\) admits an invariant diffuse measure, then \(F\) is Hermitian transversely. Moreover, admitting a ramified covering on invariant hypersurfaces of \(F\), the transverse metric can be chosen with constant curvature.