Poisson and Hamiltonian structures on complex analytic foliated manifolds

Abstract

Poisson and Hamiltonian structures are introduced in the category of complex analytic foliated manifolds endowed with a hermitian metric by analogy with the case of real foliated manifolds studied by Vaisman. A particular case of Hamiltonian structure, called tame, is proved to be induced by a Poisson bracket on the underlying manifold.