Lee Hwa Chung theorem

The Lee Hwa Chung theorem is a theorem in symplectic topology.

The statement is as follows. Let M be a symplectic manifold with symplectic form ω. Let $$\alpha$$ be a differential k-form on M which is invariant for all Hamiltonian vector fields. Then:


 * If k is odd, $$\alpha=0.$$


 * If k is even, $$\alpha = c \times \omega^{\wedge \frac{k}{2}}$$, where $$c \in \mathbb{R}.$$