论文信息 - Complexifications of holomorphic actions and the Bergman metric

Complexifications of holomorphic actions and the Bergman metric

Let G=(ℝ,+) act by biholomorphisms on a Stein manifold X which admits the Bergman metric. We show that X can be regarded as a G-invariant domain in a "universal" complex manifold X* on which the complexification of G acts. The analogous result holds for actions of a larger class of real Lie groups containing, e.g. abelian and certain nilpotent ones. For holomorphic actions of such groups on Stein manifolds, necessary and sufficient conditions for the existence of X* are given.

S. Trapani | A. Spiro | A. Iannuzzi

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