The homology theory of Koszul-Vinberg algebroids and Poisson manifolds II

We deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known whether holomorphic star products exist on complex analytic manifolds. The main purpose of this paper is to show that the concept of homology of Koszul-Vinberg algebroids on smooth (resp. complex analytic) manifolds is an effective tool to produce smooth (resp complex analytic) Poisson structures on smooth (resp. complex analytic) manifolds. We also study some invariants of contact structures which arise from the associated Koszul-Vinberg algebroids.