  The goal of this note is to exhibit the integrability properties (in the
sense of the Frobenius theorem) of holomorphic p-forms with values in certain
line bundles with seminegative curvature on a compact Kaehler manifold. There
are in fact very strong restrictions, both on the holomorphic form and on the
curvature of the seminegative line bundle. As a consequence, these observations
provide interesting information on the structure of projective manifolds which
admit a contact structure: either they are Fano manifolds or, thanks to results
of Kebekus-Peternell-Sommese-Wisniewski, they are biholomorphic to the
projectivization of the cotangent bundle of another suitable projective
manifold.
