Structure locale de variétés de Jacobi-Nijenhuis

Abstract

After a brief review on the basic notions and the principal results concerning the Jacobi manifolds, the relationship between homogeneous Poisson manifolds and conformal Jacobi manifolds, and also the compatible Jacobi manifolds, we give a generalization of some of these results needed for the contents of this paper. We introduce the notion of Jacobi-Nijenhuis structure and we study the relation between Jacobi-Nijenhuis manifolds and homogeneous Poisson-Nijenhuis manifolds. We present a local classification of homogeneous Poisson-Nijenhuis manifolds and we establish some local models of Jacobi-Nijenhuis manifolds.