Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

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

 Read article[PDF: 309KB]
Published:2014-06-16
Printed: Dec 2014
• 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 32M10 - Homogeneous complex manifolds [See also 14M17, 57T15]

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2018 : https://cms.math.ca/