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Homogeneous Kähler and Hamiltonian manifolds

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We consider actions of reductive complex Lie groups \({G=K^\mathbb{C}}\) on Kähler manifolds X such that the K-action is Hamiltonian and prove then that the closures of the G-orbits are complex-analytic in X. This is used to characterize reductive homogeneous Kähler manifolds in terms of their isotropy subgroups. Moreover we show that such manifolds admit K-moment maps if and only if their isotropy groups are algebraic.

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Correspondence to Karl Oeljeklaus.

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Dedicated to Alan T. Huckleberry.

We gratefully acknowledge that this work was partially supported by an NSERC Discovery Grant. We would also like to thank Nicolas Dutertre for valuable discussions on subanalytic geometry.

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Gilligan, B., Miebach, C. & Oeljeklaus, K. Homogeneous Kähler and Hamiltonian manifolds. Math. Ann. 349, 889–901 (2011).

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