4-dimensional anti-Kähler manifolds
type: Item
instance of: scholarly article
title: 4-dimensional anti-Kähler manifolds
zbMATH Open document ID: 1086.53091
DOI: 10.1023/B:AMHU.0000036286.72733.43
author: Hobum Kim
author: Jaeman Kim
published in: Acta Mathematica Hungarica
publication date: 2005-02-14T00:00:00Z
review text: The notion of anti-Kähler manifold is used in the sense defined in the paper by \textit{A. Borowiec, M. Francaviglia} and \textit{I. Volovich} [Differ. Geom. Appl. 12, No. 3, 281--289 (2000; Zbl 0972.53043)]. Unfortunately, the Theorems 1 and 2 stating that a 4-dimensional anti-Kählerian manifold must be Einstein and locally symmetric are not true. For instance, the metric \(g=(dz^1)^2+f(z^1)(dz^2)^2\), \(f\) being an arbitrary non-constant holomorphic function, is not Einstein and not locally symmetric. The remaining results in fact are the same as those obtained in the above cited paper by A. Borowiec et al. (loc. cit.).
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 2133952
zbMATH Keywords: anti-Kähler manifold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2133952