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Induced local actions on taut and Stein manifolds

Author: Andrea Iannuzzi
Journal: Proc. Amer. Math. Soc. 131 (2003), 3839-3843
MSC (2000): Primary 32M05, 32E10, 32Q99
Published electronically: June 30, 2003
MathSciNet review: 1999932
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Abstract: Let $G=({\mathbb{R}},+)$ act by biholomorphisms on a taut manifold $X$. We show that $X$ can be regarded as a $G$-invariant domain in a complex manifold $X^{*}$ on which the universal complexification $({\mathbb{C}},+)$ of $G$ acts. If $X$ is also Stein, an analogous result holds for actions of a larger class of real Lie groups containing, e.g., abelian and certain nilpotent ones. In this case the question of Steinness of $X^{*}$ is discussed.

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Additional Information

Andrea Iannuzzi
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italy

Keywords: Lie group actions, complexifications, taut and Stein manifolds
Received by editor(s): July 25, 2002
Published electronically: June 30, 2003
Additional Notes: This work was partially supported by the University of Bologna, funds for selected research topics
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2003 American Mathematical Society

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