Impossible world

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 $c\in \mathbb{ℝ}.$

References

• Lee, John M., Introduction to Smooth Manifolds, Springer-Verlag, New York (2003) ISBN 0-387-95495-3. Graduate-level textbook on smooth manifolds.

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