Christian Miebach
Homogeneous K\"ahler and Hamiltonian manifolds.
Mon, 01/11/2010 - 16:01 — SomNambulAuthors: Christian Miebach, Bruce Gilligan, Karl Oeljeklaus
Subjects: Complex Variables
AbstractWe consider actions of reductive complex Lie groups G=K^\mbb{C}$ on K\"ahler
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 K\"ahler 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.Spherical gradient manifolds.
Fri, 08/28/2009 - 23:56 — SomNambulAuthors: Christian Miebach, Henrik Stoetzel
Subjects: Representation Theory
AbstractWe study the action of a real-reductive group $G=K\exp(\lie{p})$ on
real-analytic submanifold $X$ of a K\"ahler manifold $Z$. We suppose that the
action of $G$ extends holomorphically to an action of the complexified group
$G^\mbb{C}$ such that the action of a maximal Hamiltonian subgroup is
Hamiltonian. The moment map $\mu$ induces a gradient map $\mu_\lie{p}\colon
X\to\lie{p}$. We show that $\mu_\lie{p}$ almost separates the $K$--orbits if
and only if a minimal parabolic subgroup of $G$ has an open orbit.
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