Summary: Noname manuscript No.
(will be inserted by the editor)
Homogeneous K¨ahler 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
K¨ahler manifolds X such that the K­action is Hamiltonian and prove then
that the closures of the G­orbits are complex-analytic in X. This is used to
characterize reductive homogeneous K¨ahler 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 × Z = S × (C

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

Collections: Mathematics