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A note on the moment map on compact Kähler manifolds

Anna Gori·Fabio Podesta'
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Abstract

We consider compact Kähler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|μ\|^2$ 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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BibTeXRIS

Anna Gori, Fabio Podesta'. 2003-10-15. A note on the moment map on compact Kähler manifolds. https://arxiv.org/abs/math/0310213

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