Poisson quasi-Nijenhuis manifolds and generalized recursion relations

Abstract: We present two involutivity theorems in the context of Poisson quasi-Nijenhuis manifolds. The second one stems from recursion relations that generalize the so called Lenard-Magri relations on a bi-Hamiltonian manifold. We apply these results to the case of the closed (or periodic) Toda lattice. Then we show how this geometrical setting is related to the bi-Hamiltonian pair of the lattice and to its recursion relations.