  In this paper, we generalize the geometry of the product pseudo-Riemannian
manifold equipped with the product Poisson structure (\cite{Nas2}) to the
geometry of a warped product of pseudo-Riemannian manifolds equipped with a
warped Poisson structure. We construct three bivector fields on a product
manifold and show that each of them lead under certain conditions to a Poisson
structure. One of these bivector fields will be called the warped bivector
field. For a warped product of pseudo-Riemannian manifolds equipped with a
warped bivector field, we compute the corresponding contravariant Levi-Civita
connection and the curvatures associated with.
