A Note on the Moment Map on Compact Kähler Manifolds
نویسنده
چکیده
We consider compact Kähler manifolds acted on by a connected compact Lie group K of isometries in a Hamiltonian fashion. We prove that the squared moment map ||μ|| is constant if and only if the manifold is biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact Kähler manifold which is acted on trivially by K. The authors do not know whether the compactness of M is essential in the main theorem; more generally it would be interesting to have a similar result for (compact) symplectic manifolds.
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تاریخ انتشار 2008