Compatibilit\'e des structures riemanniennes et des structures de Jacobi

We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, $\frac{1}{ 2}$-Kenmotsu structures and locally conformally K\"ahler structures.