Lee Hwa Chung theorem

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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 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 \Bbb{R}.

[edit] 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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