= Poisson tensor
{c}
{title2=$\pi$}
A <Poisson tensor> is a smooth bivector field defining $\{f,g\}=\pi(df,dg)$ whose bracket obeys the Jacobi identity. In coordinates, $\pi^{i\ell}\partial_\ell\pi^{jk}+\pi^{j\ell}\partial_\ell\pi^{ki}+\pi^{k\ell}\partial_\ell\pi^{ij}=0$. Its Hamiltonian distribution integrates into <symplectic leaves>, even though its rank can vary across the manifold. The tensor specifies a bracket without requiring a globally nondegenerate symplectic form.
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