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

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