Hermitian metrics of semi-negative curvature on quotients of bounded symmetric domains
type: Item
instance of: scholarly article
title: Hermitian metrics of semi-negative curvature on quotients of bounded symmetric domains
zbMATH Open document ID: 0668.53034
DOI: 10.1007/BF01393890
author: Wing-Keung To
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143666
review text: Let (X,g) be a locally symmetric Hermitian manifold of finite volume uniformized by an irreducible bounded symmetric domain of rank\(\geq 2\). Let h be a Hermitian metric on X such that (X,h) carries semi-negative curvature (i.e. its curvature tensor is semi-negative in the sense of Griffiths). Under the assumption that h is dominated by a constant multiple of g, \textit{N. Mok} [Ann. Math., II. Ser. 125, 105-152 (1987; Zbl 0616.53040)] proved that, in fact, \(h=cg\) for some constant \(c>0.\) The purpose of the present article is to prove the above result without any further assumption on the domination of h. The paper also contains a study of volume forms of negative Ricci curvature defined outside some ``partially exceptional'' divisors of a complex manifold.
reviewed by: Sorin Popescu
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 4094313
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: locally symmetric Hermitian manifold
zbMATH Keywords: volume forms
zbMATH Keywords: negative Ricci curvature
MaRDI profile type: Publication
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OpenAlex ID: W2069043742
description: scientific article; zbMATH DE number 4094313