Singular reduction of Nambu-Poisson manifolds

The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibanez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.