Self-intersection of foliation cycles on complex manifolds

Abstract

Let [Formula: see text] be a compact Kähler manifold and let [Formula: see text] be a foliation cycle directed by a transversely Lipschitz lamination on [Formula: see text]. We prove that the self-intersection of the cohomology class of [Formula: see text] vanishes as long as [Formula: see text] does not contain currents of integration along compact manifolds. As a consequence, we prove that transversely Lipschitz laminations of low codimension in certain manifolds, e.g. projective spaces, do not carry any foliation cycles except those given by integration along compact leaves.