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Lee Hwa Chung theorem

Last updated November 10, 2025

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

Statement

Lee Hwa Chung theorem—Let $M$ be a symplectic manifold with symplectic form $ω$ . Let $α$ be a differential $k$ -form on $M$ which is invariant for all Hamiltonian vector fields. Then:

If $k$ is odd, $α = 0$ .
If $k$ is even, $\alpha =c\times \omega ^{\wedge {\frac {k}{2}}}$ , where $c\in \mathbb {R}$ .

References

Lee, John M., Introduction to Smooth Manifolds, Springer-Verlag, New York (2003) ISBN 0-387-95495-3. Graduate-level textbook on smooth manifolds.
Hwa-Chung, Lee, "The Universal Integral Invariants of Hamiltonian Systems and Application to the Theory of Canonical Transformations", Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, 62(03), 237–246. doi:10.1017/s0080454100006646

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