Complexifying Lie group actions on homogeneous manifolds of non-compact dimension two

2013/10/20 by Ahmadi, S. Ruhallah, Gilligan, Bruce
#32M10 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.5378

Abstract

If X is a connected complex manifold with d_X = 2 that admits the holomorphic and transitive action of a (connected) Lie group G, then the action extends to an action of the complexification G of G on X except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is involved as base or fiber in some homogeneous fibration of X.

Related

• Proper actions of high-dimensional groups on complex manifolds
• Classical Symmetries of Complex Manifolds
• Proper group actions in complex geometry
• Complexifications of infinite-dimensional manifolds and new constructions of infinite-dimensional Lie groups
• Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms