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.
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