Poisson-Nijenhuis structures on oriented 3D-Manifolds *

We provide necessary and sufficient conditions on a (l,l)-tensor N on an oriented 3D-Poisson manifold (M, Ω, π) such that (M, π, N) is a Poisson-Nijenhuis manifold. We give a scheme for obtaining Poisson-Nijenhuis structures and also give some examples on ℝ3 and the Poisson Lie group SU (2) as an application.