Let $\,G=({\Bbb R},+)\,$ 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 $\,({\Bbb C},+)\,$ 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.

Iannuzzi, A., Spiro, A., Trapani, S. (2004). Complexifications of local actions and the Bergman metric. INTERNATIONAL JOURNAL OF MATHEMATICS, 15(8), 735-747 [10.1142/S0129167X04002533].

Complexifications of local actions and the Bergman metric

IANNUZZI, ANDREA;TRAPANI, STEFANO
2004

Abstract

Let $\,G=({\Bbb R},+)\,$ 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 $\,({\Bbb C},+)\,$ 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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
English
Con Impact Factor ISI
Iannuzzi, A., Spiro, A., Trapani, S. (2004). Complexifications of local actions and the Bergman metric. INTERNATIONAL JOURNAL OF MATHEMATICS, 15(8), 735-747 [10.1142/S0129167X04002533].
Iannuzzi, A; Spiro, A; Trapani, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31676
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