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Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two
Published online by Cambridge University Press: 20 November 2018
Abstract
If $X$ is a connected complex manifold with ${{d}_{X}}\,=\,2$ that admits a (connected) Lie group $G$ acting transitively as a group of holomorphic transformations, then the action extends to an action of the complexification $\widehat{G}$ of $G$ on $X$ except when either the unit disk in the complex plane or a strictly pseudoconcave homogeneous complex manifold is the base or fiber of some homogeneous fibration of $X$.
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- Copyright © Canadian Mathematical Society 2014