COMPACT ORBITS OF PARABOLIC SUBGROUPS

Abstract We study the action of a real reductive group G on submanifold X Kähler manifold Z . suppose that compact connected Lie U with algebra $\mathfrak {u}$ extends holomorphically to an complexified $U^{\mathbb {C}}$ and -action is Hamiltonian. If $G\subset U^{\mathbb compatible, there exists gradient map $\mu _{\mathfrak p}:X \longrightarrow \mathfrak p$ where g=\mathfrak k \oplus Cartan decomposition g$ In this paper, we describe orbits parabolic subgroups in terms p}$