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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

S. Ruhallah Ahmadi  and
Bruce Gilligan
S. Ruhallah Ahmadi
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2 e-mail: seyed.ruhala.ahmadi@gmail.comgilliganbc@gmail.com
Bruce Gilligan
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2 e-mail: seyed.ruhala.ahmadi@gmail.comgilliganbc@gmail.com
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Abstract

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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

32M10homogeneous complex manifoldnon-compact dimension twocomplexification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 673 - 682
Copyright
Copyright © Canadian Mathematical Society 2014

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