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Homogeneous Kähler and Hamiltonian manifolds

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina, Regina, S4S 0A2, Canada

    Bruce Gilligan

  2. LATP-UMR(CNRS) 6632, CMI-Université d’Aix-Marseille I, 39, rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Christian Miebach & Karl Oeljeklaus

Authors
  1. Bruce Gilligan
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  2. Christian Miebach
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  3. Karl Oeljeklaus
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Corresponding author

Correspondence to Karl Oeljeklaus.

Additional information

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). https://doi.org/10.1007/s00208-010-0546-y

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  • DOI: https://doi.org/10.1007/s00208-010-0546-y

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