We consider compact K\¨ahler manifolds acted on effectively by a connected compact Lie group K of isometries 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 biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact K\¨ahler manifold which is acted on trivially by K.
A note on the moment map on compact Kaehler manifolds / A. Gori, F. Podestà. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 26:3(2004), pp. 315-318. [10.1023/B:AGAG.0000042928.71614.3a]
A note on the moment map on compact Kaehler manifolds
A. GoriPrimo
;
2004
Abstract
We consider compact K\¨ahler manifolds acted on effectively by a connected compact Lie group K of isometries 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 biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact K\¨ahler manifold which is acted on trivially by K.
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