Nonexistence of Levi flat hypersurfaces with positive normal bundle in compact Kähler manifolds of dimension ≥3.

Let X be a compact connected Kähler manifold of dimension ≥ 3 and L a C ∞ 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. [ABSTRACT FROM AUTHOR]