Definition
Let be a Poisson manifold (that is is a multi-vector field such that ).
Using the bivector field, is a singular distribution, and the dimension of is constant on flow lines of Hamiltonian vector fields, so the distribution is integrable.
Then the leaves of the foliation that come from integrating the distribution are called the symplectic leaves of the Poisson manifold.
Symplectic Structure
Let be the foliation of induced by .
Then a symplectic leaf has a symplectic structure defined at by