Polarized Poisson structures (Q2051350)

Following earlier work by the first author, the paper under review introduces polarized Poisson structures on a foliated manifold \((M,\mathcal{F})\), where \(\mathcal{F}\) is a coisotropic foliation. It is then shown that the characteristic distribution spanned by the polarized Hamiltonian vector fields is integrable. A special case is when \(\mathcal{F}\) is a Lagrangian foliation of the polarized Poisson structure. In this case the characteristic distribution has constant rank, whence integrability follows from the classical Frobenius theorem.