Abstract
We consider compact Kähler manifolds acted on effectively by a connected compact Lie group K of isometries 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 biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact Kähler manifold which is acted on trivially by K.
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Gori, A., Podestà, F. A Note on the Moment Map on Compact Kähler Manifolds. Annals of Global Analysis and Geometry 26, 315–318 (2004). https://doi.org/10.1023/B:AGAG.0000042928.71614.3a
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DOI: https://doi.org/10.1023/B:AGAG.0000042928.71614.3a