On Hermitian surfaces with \(J\)-invariant Ricci tensor
type: Item
instance of: scholarly article
title: On Hermitian surfaces with \(J\)-invariant Ricci tensor
zbMATH Open document ID: 1010.53055
author: R. Smith
published in: Journal of Geometry
publication date: 2003-05-05T00:00:00Z
review text: Let \(M(J,g)\) be a compact Hermitian surface. Let \(s\) denote the usual scalar curvature of \(M(J,g)\), and \(k\) its conformal scalar curvature. By definition, \(k\) is the scalar curvature with respect to \(g\) of the canonical Weyl structure associated to the Hermitian structure \((J,g)\). The main result states that if the Ricci tensor of \(g\) is \(J\)-invariant and the difference \(s-k\) is constant, then \(M(J,g)\) must be Kähler.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1760632
zbMATH Keywords: Hermitian manifold
zbMATH Keywords: Kähler manifold
MaRDI profile type: Publication
full work available at URL: s00022-001-8576-y
OpenAlex ID: W2053682711
DOI: 10.1007/S00022-001-8576-Y
description: scientific article; zbMATH DE number 1760632