Foliations and CR geometry

I will discuss holomorphic foliations on a complex manifold from the point of view of the exceptional minimal set conjecture. In particular I am interested in curvature conditions for the holomorphic normal bundle of the foliation. The main result is that if the holomorphic normal bundle is positive in the sense of Griffiths, then the foliation does not admit a compact invariant set that is a complete intersection of smooth real hypersurfaces. As a by-product, we obtain classification results for compact Levi-flat CR manifolds.