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Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two

  • S. Ruhallah Ahmadi,
    Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2
  • Bruce Gilligan,
    Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2
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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 $X$.
Keywords: homogeneous complex manifold, non-compact dimension two, complexification homogeneous complex manifold, non-compact dimension two, complexification
MSC Classifications: 32M10 show english descriptions Homogeneous complex manifolds [See also 14M17, 57T15] 32M10 - Homogeneous complex manifolds [See also 14M17, 57T15]
 

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