 
Summary: Noname manuscript No.
(will be inserted by the editor)
Homogeneous Kšahler and Hamiltonian manifolds
Bruce Gilligan · Christian Miebach ·
Karl Oeljeklaus
Dedicated to Alan T. Huckleberry
Received: date / Accepted: date
Abstract We consider actions of reductive complex Lie groups G = KC
on
Kšahler manifolds X such that the Kaction is Hamiltonian and prove then
that the closures of the Gorbits are complexanalytic in X. This is used to
characterize reductive homogeneous Kšahler manifolds in terms of their isotropy
subgroups. Moreover we show that such manifolds admit Kmoment maps if
and only if their isotropy groups are algebraic.
Mathematics Subject Classification (2000) 32M05; 32M10; 53D20
1 Introduction
A reductive complex Lie group G is a complex Lie group admitting a compact
real form K, i. e. G = KC
. Equivalently a finite covering of G is of the form
S Ś Z = S Ś (C
