Compatibility of a Jacobi structure and a Riemannian structure on a Lie algebroid

Abstract: In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, (1/2)-Kenmotsu structures and locally conformally K\"ahler structures. In this paper we are generalizing this work to the framework of Lie algebroids.