Compact Kähler surfaces with harmonic anti-self-dual Weyl tensor.
type: Item
instance of: scholarly article
title: Compact Kähler surfaces with harmonic anti-self-dual Weyl tensor.
zbMATH Open document ID: 1037.53028
DOI: 10.1016/S0926-2245(02)00076-1
author: Włodzimierz Jelonek
published in: Differential Geometry and its Applications
publication date: 2002-08-14T00:00:00Z
review text: The author proves the following theorem: Let \((M, g, J)\) be a compact Kähler surface with harmonic anti-self-dual Weyl tensor \((\delta W^-=0)\). Then \(M\) has constant scalar curvature (and thus is Einstein or is locally a product of two Riemannian surfaces with constant sectional curvature) or is a ruled surface with extremal Kähler metric with non-constant scalar curvature which admits an opposite Hermitian structure \(\overline J\) such that \((M, g,\overline J)\) satisfies a \((G_2)\) condition of Gray and is conformal to an extremal Kähler surface.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1780874
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: ruled surface
zbMATH Keywords: extremal Kähler surface
reviewed by: Domenico Perrone
MaRDI profile type: Publication
Wikidata QID: Q115338193
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full work available at URL: s0926-2245(02)00076-1
OpenAlex ID: W2078757732
description: scientific article; zbMATH DE number 1780874