  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.
