Abstract
AbstractIf X is a connected complex manifold with dX = 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 Ĝ 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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