Impossible world: Difference between revisions

Latest revision as of 06:53, 25 September 2013

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:

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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+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>\alpha</math> be a [[Differential form|differential ''k''-form]] on ''M'' which is invariant for all [[Hamiltonian vector field]]s. Then:
+:*If ''k'' is odd, <math>\alpha=0.</math>
+:*If ''k'' is even, <math>\alpha = c \times \omega^{\wedge \frac{k}{2}}</math>, where <math>c \in \Bbb{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.
+[[Category:Symplectic geometry]]
+[[Category:Theorems in topology]]
+[[Category:Theorems in geometry]]
+{{differential-geometry-stub}}