Locally conformally flat Kähler and para-Kähler manifolds
type: Item
instance of: scholarly article
title: Locally conformally flat Kähler and para-Kähler manifolds
zbMATH Open document ID: 1469.53070
author: M. Ferreiro-Subrido
author: Eduardo García-Río
author: R. Vázquez-Lorenzo
published in: Annals of Global Analysis and Geometry
publication date: 2021-06-14T00:00:00Z
review text: Let \((M,g,J_\epsilon)\) be a (para-)Kähler manifold, where \(J_\epsilon\) denotes the parallel (para-)complex structure, \(J_\epsilon^2 =-\epsilon \operatorname{Id}\) and \(g(J_\epsilon X,J_\epsilon Y) =\epsilon g(X,Y)\) for \(\epsilon =\pm 1\). The authors complete the classification of locally conformally flat Kähler and para-Kähler manifolds, describing all possible non-flat curvature models for Kähler and para-Kähler surfaces.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 7358592
zbMATH Keywords: Kähler surface
zbMATH Keywords: para-Kähler surface
zbMATH Keywords: conformal flatness
zbMATH Keywords: Walker structure
zbMATH Keywords: Riemannian extension
zbMATH Keywords: affine surface
reviewed by: Nicolai K. Smolentsev
MaRDI profile type: Publication
full work available at URL: s10455-021-09755-8
OpenAlex ID: W3133676787
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DOI: 10.1007/S10455-021-09755-8
description: scientific article; zbMATH DE number 7358592