Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kahler manifolds of dimension 3

Let X be a compact connected Milder manifold of dimension >= 3 and L a C-infinity Levi flat hypersurface in X. Then the normal bundle to the Levi foliation does not admit a Hermitian metric with positive curvature along the leaves. This represents an answer to a conjecture of Marco Brunella.