Advanced Search

We study the action of a real-reductive group $G=Kexp\left(𝔭\right)$ on a real-analytic submanifold $X$ of a Kähler manifold. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^{ℂ}$ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map ${\mu }_{𝔭}:X\to 𝔭$. We show that ${\mu }_{𝔭}$ almost separates the $K$–orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion’s characterization of spherical...