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Let $N$ be a homogeneous space. Therefore we find a Liegroup $G$ and a isotropy-subgroup $K$ of $G$, such that we can identify $N = G/K$. Then we have a canonical action $l\colon G \times G/K \to G/K$ ...

A Kaehler Hamiltonian G-manifold is a Kaehler manifold with a Hamiltonian G-action, i.e., a G-action generated by a moment map. In particular, the Killing vector fields which generate the G-action are ...