On Norden metrics which are locally conformal to anti-Kählerian metrics
type: Item
instance of: scholarly article
title: On Norden metrics which are locally conformal to anti-Kählerian metrics
zbMATH Open document ID: 0969.53013
DOI: 10.1023/A:1006354630911
author: Sorin Dragomir
author: M. Francaviglia
published in: Acta Applicandae Mathematicae
publication date: 2001-10-01T00:00:00Z
review text: A Norden manifold is a triplet \((M,J,g)\) where \(M\) is a smooth manifold, \(J\) is an almost complex structure on \(M\) (i.e., \(J^2= -id)\) and \(g\) is a necessarily pseudo-Riemannian metric of signature \((n,n)\) on \(M\) such that \(J\) becomes an anti-isometry at each point (i.e., \(g(JX,JY)= -g(X,Y)\) for all \(X,Y\in{\mathfrak X}(M)\)). A Norden structure \((J,g)\) is said to be anti-Kähler if \(\nabla J= 0\), where \(\nabla\) is the Levi-Civita connection of \(g\), and it is said to be locally conformally anti-Kähler if there exist local conformal deformations \(e^ug\) of \(g\) such that \((J,e^ug)\) becomes anti-Kähler on some open \({\mathfrak U}\subset M\). The authors' main concern is the construction of examples of locally conformally anti-Kähler structures on \(\Sigma\times S^1\), where \(\Sigma\) is either a pseudo-sphere of a pseudo-hyperbolic space, which are not anti-Kähler.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1506489
zbMATH Keywords: locally conformally anti-Kähler
zbMATH Keywords: Lee field
zbMATH Keywords: Norden manifold
zbMATH Keywords: almost complex structure
zbMATH Keywords: pseudo-Riemannian metric
zbMATH Keywords: anti-Kähler structures
reviewed by: Eduardo García-Río
MaRDI profile type: Publication
full work available at URL: a:1006354630911
OpenAlex ID: W135724582
description: scientific article; zbMATH DE number 1506489