Recall that any bivector field can be regarded as a skew homomorphism \pi^{\sharp}: T^{*} M \to T M, \alpha \mapsto \pi(\alpha,\cdot) . The image {\pi^{\sharp}}(T^{*} M) \subset TM consists therefore of the values {X_{f}}(x) of all Hamiltonian vector fields evaluated at every x \in M .
