Homogeneous Kähler and Hamiltonian manifolds

Bruce Gilligan (1) , Christian Miebach (2) , Karl Oeljeklaus (2)

1 Dep. of Mathematics and Statistics
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider actions of reductive complex Lie groups G=K^\mbb{C}$ on Kähler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that all $G$--orbits are locally closed 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.

Domaines: Variables complexes [math.CV]

Bruce Gilligan, Christian Miebach, Karl Oeljeklaus. Homogeneous Kähler and Hamiltonian manifolds. 2010. ⟨hal-00445106v1⟩