Compatibility of Riemannian structures and Jacobi structures

TL;DR

This paper introduces a compatibility concept between Riemannian and Jacobi structures, showing how classical examples like Poisson, contact, and locally conformally symplectic structures relate to specific Riemannian structures.

Contribution

It defines a new notion of compatibility and connects classical Jacobi structures with known Riemannian structures in a unified framework.

Findings

Poisson structures correspond to Riemann-Poisson structures

Contact structures relate to 1/2-Kenmotsu structures

Locally conformally symplectic structures relate to locally conformally Kähler structures

Abstract

We give a notion of compatibility between a Riemannian structure and a Jacobi structure. We prove that in 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 Kahler structures.