ON THE COEFFECTIVE COHOMOLOGY OF COMPACT SYMPLECTIC-MANIFOLDS

The coeffective cohomology of compact symplectic manifolds has recentl y been studied by T. Bouche. In fact, the coeffective cohomology gives a new obstruction for a symplectic manifold to be Kahler. In this Not e we exhibit an example of compact symplectic non-Kahler manifold whic h does not satisfy Bouche's condition. Moreover, since this manifold a dmits an indefinite Kahler metric we deduce that Bouche's condition fa ils also for compact manifolds with an indefinite Kahler metric.