Geodesic
Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 673-682

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DOI

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 $X$ .
DOI : 10.4153/CMB-2014-028-6
Mots-clés : 32M10, homogeneous complex manifold, non-compact dimension two, complexification 
Ahmadi, S. Ruhallah; Gilligan, Bruce. Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 673-682. doi: 10.4153/CMB-2014-028-6
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     title = {Complexifying {Lie} {Group} {Actions} on {Homogeneous} {Manifolds} of {Non-compact} {Dimension} {Two}},
     journal = {Canadian mathematical bulletin},
     pages = {673--682},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2014-028-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-028-6/}
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