Curvature characterization of certain bounded domains of holomorphy
type: Item
instance of: scholarly article
title: Curvature characterization of certain bounded domains of holomorphy
zbMATH Open document ID: 0788.53067
published in: Pacific Journal of Mathematics
publication date: 1994-05-24T00:00:00Z
review text: The author studies the relation between the existence of a negatively curved complete hermitian metric on a complex manifold \(M\) and the product structure of (or contained in) \(M\). He introduces the concept of geometric ranks and gives a curvature characterization of the rank one manifolds, which generalizes previous results of P. Yang and N. Mok. It is proved, for example, that the product of two bounded domains of holomorphy does not admit any complete Kähler metric with bisectional curvature bounded between two negative constants. The old techniques of Yau's Schwartz lemma and Cheng-Yau's result on the existence of Kähler- Einstein metrics are used in the proofs.
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 537380
zbMATH Keywords: negative bisectional curvature
zbMATH Keywords: hermitian metric
zbMATH Keywords: product structure
zbMATH Keywords: complete Kähler metric
zbMATH Keywords: Schwartz lemma
author: Fangyang Zheng
MaRDI profile type: Publication
full work available at URL: pjm.1994.163.183
OpenAlex ID: W2078757870
DOI: 10.2140/PJM.1994.163.183
description: scientific article; zbMATH DE number 537380