Local structure of Jacobi--Nijenhuis manifolds (Q1867209)

The notion of Jacobi-Nijenhus structure was first introduced by \textit{J. C. Marrero, J. Monterde} and \textit{E. Padron} in [C. R. Acad. Sci., Paris, Sér I Math 329, 797-802 (1999; Zbl 0949.37056)]. In this paper a stricter definition of this notion is proposed and the relation between Jacobi-Nijenhuis manifolds and homogeneous Poisson-Nijenhuis manifolds is studied. The authors also present a local classification of homogeneous Poisson-Nijenhuis manifolds and establish some local models of Jacobi-Nijenhuis manifolds. These provide a hope that this new structure will play a part as important as Poisson, Jacobi and Poisson-Nijenhuis structures in the study of integrable systems.