Dirac-nijenhuis structures on lie bialgebroids

This paper is a continuation of the work done in [1]. We define Dirac-Nijenhuis structures (DN structures) on Lie bialgebroids, a generalization of the notion of Dirac-Nijenhuis structures on manifolds given in [1]. However, the problems we are going to deal with are more complex than the ones in [1]. The necessary and sufficient conditions for a structure to be a DN structure on a Lie bialgebroid as well as several examples of these structures are given. At the end of the paper we discuss the fundamental sections of DN structures.