Compact orbits of Parabolic subgroups

2021/05/12 by Biliotti, Leonardo, Windare, Joshua O.
#32M05 #57S20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.05765

Abstract

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

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