  We show that, for any regular Poisson manifold, there is an injective natural
linear map from the first leafwise cohomology space into the first Poisson
cohomology space which maps the Reeb class of the symplectic foliation to the
modular class of the Poisson manifold. The Riemannian interpretation of those
classes will permit us to show that a regular Poisson manifold whose symplectic
foliation is of codimension one is unimodular if and only if its symplectic
foliation is Riemannian foliation. It permit us also to construct examples of
unimodular Poisson manifolds and other which are not unimodular. Finally, we
prove that the first leafwise cohomology is an invariant of Morita equivalence.
