A CHARACTERIZATION OF C<sup>k</sup>×(C*)<sup>ℓ</sup>FROM THE VIEWPOINT OF BIHOLOMORPHIC AUTOMORPHISM GROUPS

Akio Kodama, Satoru Shimizu

Type: Article

Publication Date: 2003-05-06

Citations: 0

DOI: https://doi.org/10.4134/jkms.2003.40.3.563

Abstract

We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to <TEX>$Aut(C^k {\times}(C^*)^{n - k})$</TEX> as topological groups, then M itself is biholomorphically equivalent to <TEX>C^k{\times}(C^*)^{n - k}$</TEX>. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.

Locations

Journal of the Korean Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	Characterization of ${\bf C}^n$ by its automorphism group	2000	Alexander Isaev
+	A group-theoretic characterization of the direct product of a ball and a Euclidean space	2006	Jisoo Byun Akio Kodama Satoru Shimizu
+	Characterization of the unit ball in ${\bf C}^n$ among complex manifolds of dimension $n$	2004	Alexander Isaev
+	Developments in Oka theory since 2017.	2020	Franc Forstnerič
+	A group-theoretic characterization of the Fock-Bargmann-Hartogs domains	2019	Akio Kodama
+ PDF Chat	A group-theoretic characterization of the space obtained by omitting the coordinate hyperplanes from the complex Euclidean space, II	2006	Akio Kodama Satoru Shimizu
+	Automorphisms of Complex Euclidean Spaces	2017	Franc Forstnerič
+	Recent developments on Oka manifolds	2020	Franc Forstnerič
+	Stein Manifolds and Holomorphic Mappings	2017	Franc Forstnerič
+	A family of complex manifolds covered by δ<sub>n</sub>	1998	Chiara De Fabritiist
+ PDF Chat	An intrinsic characterization of the direct product of balls	2009	Akio Kodama Satoru Shimizu
+	Automorphisms of $\mathbb C^k$ and associated compact complex manifolds	2005	Julie Renaud
+	Infinite-dimensionality of the Automorphism Groups of Homogeneous Stein Manifolds	2008	Alan Huckleberry Alexander Isaev
+	On the automorphism group of a stein manifold	1983	Eric Bedford
+ PDF Chat	Stein Structures: Existence and Flexibility	2014	Kai Cieliebak Yakov Eliashberg
+ PDF Chat	Diffeomorphisms of Stein structures	2006	Klas Diederich Alexandre Sukhov
+	Recent developments on Oka manifolds	2023	Franc Forstnerič
+	Stein structures: existence and flexibility	2013	Kai Cieliebak Yakov Eliashberg
+	On Automorphisms of Complex $$b^k$$-Manifolds	2024	Tatyana Barron Michael Francis
+ PDF Chat	Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds	2015	Filippo Bracci Andrea Iannuzzi Benjamin McKay

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (7)

Action	Title	Year	Authors
+	HOLOMORPHIC AUTOMORPHISMS OF HYPERBOLIC REINHARDT DOMAINS	1989	N. G. Kruzhilin
+ PDF Chat	Automorphisms and equivalence of bounded Reinhardt domains not containing the origin	1988	Satoru Shimizu
+	Deformations of strictly pseudoconvex domains	1978	D. Burns Steven Shnider Raymond O. Wells
+ PDF Chat	T n -actions on holomorphically separable complex manifolds	1989	David E. Barrett Eric Bedford Jiri Dadok
+	Determination of a Domain in Complex Space by its Automorphism Group	2002	Steven G. Krantz
+ PDF Chat	Effective Actions of the Unitary Group on Complex Manifolds	2002	A. V. Isaev N. G. Kruzhilin
+	Deformation of complex structures, estimates for the ∂ equation, and stability of the Bergman kernel	1982	Robert E. Greene Steven G. Krantz