= Symplectic foliation
The <symplectic foliation> of a <Poisson manifold> consists of maximal connected integral manifolds of its Hamiltonian distribution. Each leaf has a nondegenerate closed two-form inverse to the restricted Poisson structure, with compatible sign conventions. Ranks can differ between leaves, making this a singular foliation. Hamiltonian flows remain within a leaf, and <Casimir functions of a Poisson manifold> are constant along every leaf; a Casimir level set need not be a single leaf.
Back to article page
