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

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