2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115208We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces classical integrable hierarchies.26 pages, 27 references. One major change: the assumption on non-degeneracy of the Poisson tensor on a PN manifold was dropped. Several minor changes and 2 new references includedDifferential GeometryMathematical Physics53D17, 37J35text