Lee Hwa Chung theorem

Short description: Characterizes differential k-forms which are invariant for all Hamiltonian vector fields

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 [math]\displaystyle{ \alpha }[/math] be a differential k-form on M which is invariant for all Hamiltonian vector fields. Then:

• If k is odd, [math]\displaystyle{ \alpha=0. }[/math]

• If k is even, [math]\displaystyle{ \alpha = c \times \omega^{\wedge \frac{k}{2}} }[/math], where [math]\displaystyle{ c \in \mathbb{R}. }[/math]

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