On the Integrability of Orthogonal Distributions in Poisson Manifolds
  We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided. 
Dan Fish, Serge Preston