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A splitting result for compact symplectic manifolds

Lucio Bedulli·Anna Gori
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Abstract

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 $||μ||^2$ 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-Kähler setting the symplectomorphism turns out to be an isometry.

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Lucio Bedulli, Anna Gori. 2004-12-02. A splitting result for compact symplectic manifolds. https://arxiv.org/abs/math/0412056

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