A splitting result for compact symplectic manifolds

Details A splitting result for compact symplectic manifolds A splitting result for compact symplectic manifolds

2004-12-02

arxiv.org/abs/math/0412056v1

Results Math. 47 (2005), n. 3-4, 194-198.

Mathematics

Symplectic Geometry

5 pages, no figures

Scientific paper

We consider compact symplectic manifolds acted on effectively by a compact connected Lie group $K$ in a Hamiltonian fashion. We prove that the squared moment map $||\mu||^2$ is constant if and only if $K$ is semisimple and the manifold is $K$-equivariantly symplectomorphic to a product of a flag manifold and a compact symplectic manifold which is acted on trivially by $K$. In the almost-K\"ahler setting the symplectomorphism turns out to be an isometry.

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