Symplectic A-directed immersions

We prove a symplectic analogue of A-directed immersion theorem for exact symplectic manifolds and generalize this result to closed manifolds under a completeness hypothesis. As an application we have derived a sufficient condition for the existence of a Poisson structure on an exact symplectic manifold with a codimension-2q characteristic foliation such that the Poisson structure is induced from the ambient symplectic structure.