  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.
