On the symplectic realization of Poisson-Nijenhuis manifolds

Abstract

We consider the problem of the symplectic realization of a Poisson-Nijenhuis manifold. By applying a new technique developed by M. Crainic and I. Marcut for the study of the above problem in the case of a Poisson manifold, we establish the existence, under a condition, of a nondegenerate Poisson-Nijenhuis structure on an open neighborhood of the zero-section of the cotangent bundle of the manifold, which symplectizes the initial structure. Additionally, we present some examples.