Mathematische Annalen

, Volume 349, Issue 4, pp 889–901 | Cite as

Homogeneous Kähler and Hamiltonian manifolds

  • Bruce Gilligan
  • Christian Miebach
  • Karl Oeljeklaus
Article

Abstract

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.

Mathematics Subject Classification (2000)

32M05 32M10 53D20 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Bruce Gilligan
    • 1
  • Christian Miebach
    • 2
  • Karl Oeljeklaus
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada
  2. 2.LATP-UMR(CNRS) 6632, CMI-Université d’Aix-Marseille IMarseille Cedex 13France

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