Quasi-Lie Bialgebroids, Dirac Structures, and Deformations of Poisson Quasi-Nijenhuis Manifolds

Abstract

We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.