  Riemann Poisson manifolds were introduced by the author in [1] and studied in
more details in [2]. K\"ahler-Riemann foliations form an interesting subset of
the Riemannian foliations with remarkable properties (see [3]).
  In this paper we will show that to give a regular Riemann Poisson structure
on a manifold $M$ is equivalent to to give a K\"ahler-Riemann foliation on $M$
such that the leafwise symplectic form is invariant with respect to all local
foliate perpendicular vector fields. We show also that the sum of the vector
space of leafwise cohomology and the vector space of basic forms is a subspace
of the space of Poisson cohomology.
