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

#### 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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Moment map
Settore MAT/03 - Geometria
2004
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/163169
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