Jacobi structures with background.

Combining the twisted Jacobi structure [Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids, J. Phys. A: Math. Gen. 39(33) (2006) 10449- 10475] with that of a Poisson structure with a 3-form background [Poisson geometry with a 3-form background, Prog. Theor. Phys. Suppl. 144 (2001) 145-154], alias twisted Poisson, we propose and analyze a new structure, called Jacobi structure with background. The background is a pair consisting of a 3-form and a 2-form. We describe their characteristic leaves. For twisted contact dual pairs, we show the correspondence of characteristic leaves of the two Jacobi manifolds with background. [ABSTRACT FROM AUTHOR]