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arXiv · 1310.5378

Complexifying Lie group actions on homogeneous manifolds of non-compact dimension two

S. Ruhallah Ahmadi·Bruce Gilligan
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Abstract

If $X$ is a connected complex manifold with $d_X = 2$ that admits the holomorphic and transitive action of a (connected) Lie group $G$, then the action extends to an action of the complexification $\hat{G}$ of $G$ on $X$ except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is involved as base or fiber in some homogeneous fibration of $X$.

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S. Ruhallah Ahmadi, Bruce Gilligan. 2013-10-20. Complexifying Lie group actions on homogeneous manifolds of non-compact dimension two. https://arxiv.org/abs/1310.5378

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