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

TL;DR

This paper introduces a compatibility concept between Riemannian metrics and Jacobi structures, linking classical geometric structures like Poisson, contact, and locally conformally symplectic to Riemannian geometry.

Contribution

It defines a new compatibility notion and connects key Jacobi structures to known Riemannian geometric frameworks.

Findings

Poisson structures correspond to Riemann-Poisson structures

Contact structures relate to $rac{1}{2}$-Kenmotsu structures

Locally conformally symplectic structures connect to locally conformally Kähler structures

Abstract

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.