Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-03-07116-8
Published electronically: June 30, 2003
MathSciNet review: 1999932
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [A] M. Abate, Iteration Theory of Holomorphic Maps on Taut Manifolds, Research and Lecture Notes in Mathematics. Complex Analysis and Geometry, Mediterranean Press, Cosenza, 1989. MR 92i:32032
  • [CIT] E. Casadio Tarabusi, A. Iannuzzi, and S. Trapani, Globalizations, fiber bundles and envelopes of holomorphy, Math. Z. 233 (2000), 535-551. MR 2001f:32035
  • [DG] F. Docquier and H. Grauert, Leisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123. MR 26:6435
  • [F] F. Forstneric, Actions of $({\mathbb{R}},+)$ and $({\mathbb{C}},+)$ on complex manifolds, Math. Z. 223 (1996), 123-153. MR 97i:32041
  • [GH] B. Gilligan and A. T. Huckleberry, On non-compact complex nil-manifolds, Math. Ann. 238 (1978), 39-49. MR 80a:32021
  • [GR] H. Grauert and R. Remmert, Coherent Analytic Sheaves, Grundlehren der Mathematischen Wissenschaften, Vol. 265, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984. MR 86a:32001
  • [H] P. Heinzner, Geometric invariant theory on Stein spaces, Math. Ann. 289 (1991), 631-662. MR 92j:32116
  • [HI] P. Heinzner and A. Iannuzzi, Integration of local actions on holomorphic fiber spaces, Nagoya Math. J. 146 (1997), 31-53. MR 98k:32047
  • [I] A. Iannuzzi, Characterizations of $\,G$-tube domains, Manuscripta Math. 98 (1999), 425-445. MR 2000e:32034
  • [Ma] A. I. Mal $\mathsurround 0pt'$cev, On a class of homogeneous spaces, Amer. Math. Soc. Translation, vol. 39, Amer. Math. Soc., Providence, RI, 1951. MR 12:589e
  • [P] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc., vol. 22, Amer. Math. Soc., Providence, RI, 1957. MR 22:12162
  • [V] V. S. Vladimirov, Les fonctions de plusieurs variables complexes et leur application à la théorie quantique des champs, Dunod, Paris, 1967. MR 36:1692

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32M05, 32E10, 32Q99

Retrieve articles in all journals with MSC (2000): 32M05, 32E10, 32Q99


Additional Information

Andrea Iannuzzi
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italy
Email: iannuzzi@dm.unibo.it

DOI: https://doi.org/10.1090/S0002-9939-03-07116-8
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

American Mathematical Society