Conformal duality and compact complex surfaces
type: Item
instance of: scholarly article
title: Conformal duality and compact complex surfaces
zbMATH Open document ID: 0571.32017
DOI: 10.1007/BF01457232
author: Charles P. Boyer
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164115
review text: Let M be a compact complex surface with first Betti number \(b_ 1\) which admits a compatible anti-self-dual metric g. In this paper we prove that if \(b_ 1\) is even, then g is conformally equivalent to a Kähler metric with zero scalar curvature and if \(b_ 1\) is odd then g is conformally equivalent to a locally conformally Kähler metric with positive scalar curvature. Applying this result to the Enriques-Kodaira classification of compact complex surfaces, we give a list of possible surfaces which admit an anti-self-dual metric.
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 14J15
zbMATH DE Number: 3910767
zbMATH Keywords: anti-self-dual metric
zbMATH Keywords: Kähler metric
zbMATH Keywords: classification of compact complex surfaces
MaRDI profile type: Publication
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OpenAlex ID: W1988143916
description: scientific article; zbMATH DE number 3910767