Supplement to ``Fine structure of reductive pseudo-Kählerian spaces''
type: Item
instance of: scholarly article
title: Supplement to ``Fine structure of reductive pseudo-Kählerian spaces''
zbMATH Open document ID: 0799.53058
DOI: 10.1007/BF00147553
author: Daniel Guan
author: Josef F. Dorfmeister
published in: Geometriae Dedicata
publication date: 1992-09-27T00:00:00Z
review text: The authors correct the proof of some statement of the paper [Geom. Dedicata 39, No. 3, 321-338 (1991; Zbl 0739.53040)] and derive from the results of the paper a new corollary: Let \(M=G/H\) be a reductive homogeneous pseudo-Kähler manifold. Then its fibration by bounded holomorphic functions is a trivial holomorphic fiber bundle over a bounded symmetric domain whose fiber is a reductive pseudo-Kähler manifold with no nonconstant bounded holomorphic functions. In particular, if any two points of \(M\) can be separated by holomorphic functions, than it is biholomorphic to \({\mathbb{C}}^ n\times({\mathbb{C}}^*)^ m\times D\), where \(D\) is a bounded symmetric domain.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 57587
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: pseudo-Kähler manifolds
zbMATH Keywords: bounded symmetric domains
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147553
OpenAlex ID: W2092087919
description: scientific article; zbMATH DE number 57587