COMPACT ORBITS OF PARABOLIC SUBGROUPS
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Abstract We study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of a compact connected Lie group U with Lie algebra $\mathfrak {u}$ extends holomorphically to an action of the complexified group $U^{\mathbb {C}}$ and that the U-action on Z is Hamiltonian. If $G\subset U^{\mathbb {C}}$ is compatible, there exists a gradient map $\mu _{\mathfrak p}:X \longrightarrow \mathfrak p$ where $\mathfrak g=\mathfrak k \oplus \mathfrak p$ is a Cartan decomposition of $\mathfrak g$ . In this paper, we describe compact orbits of parabolic subgroups of G in terms of the gradient map $\mu _{\mathfrak p}$ .
2008 ◽
Vol 144
(1)
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pp. 163-185
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2013 ◽
Vol 2013
(679)
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pp. 223-247
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1989 ◽
Vol 114
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pp. 77-122
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1968 ◽
Vol 31
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pp. 105-124
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2011 ◽
Vol 148
(3)
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pp. 807-834
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