On the sum of the Hermitian scalar curvatures of a compact Hermitian manifold
type: Item
instance of: scholarly article
title: On the sum of the Hermitian scalar curvatures of a compact Hermitian manifold
zbMATH Open document ID: 0602.53041
DOI: 10.1007/BF01161768
author: Andrew Balas
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183704
review text: In this brief paper we prove that if the sum of the two Hermitian scalar curvatures is positive at every point of a compact Hermitian manifold, then all the plurigenera of the manifold vanish. As an application we show that if a compact Hermitian manifold of complex dimension 2 or 3 has positive holomorphic sectional curvature at every point then here also all the plurigenera of the manifold vanish. Weaker results are obtained if the quantities are assumed to be only nonnegative.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 3971674
zbMATH Keywords: scalar curvatures
zbMATH Keywords: Hermitian manifold
zbMATH Keywords: holomorphic sectional curvature
zbMATH Keywords: plurigenera
MaRDI profile type: Publication
cites work: Compact Hermitian manifolds of constant holomorphic sectional curvature
cites work: Fibrés hermitiens à endomorphisme de Ricci non négatif
cites work: Q4136133
description: scientific article; zbMATH DE number 3971674