Yang-Mills theory and uniformization
type: Item
instance of: scholarly article
title: Yang-Mills theory and uniformization
zbMATH Open document ID: 0635.32017
DOI: 10.1007/BF00402147
author: Carlos Simpson
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: Consider a stable holomorphic vector bundle over a compact, Hermitian manifold. For various hypothesis concerning the dimension of the manifold and whether or not it is Kähler it has been shown by Narasimhan and Seshadri, Donaldson, Uhlenbeck and Yau and Buchdahl that the bundle admits a Hermitian-Yang-Mills connection. In this paper the author introduces the concept of a stable system of Hodge bundles and proves that over a Kähler manifold it admits a Hermitian-Yang-Mills connection. If certain chern classes vanish this leads to a complex variation of the Hodge structure and thereby a criterion for the manifold to be uniformized by a bounded symmetric domain.
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4034117
zbMATH Keywords: stable holomorphic vector bundle
zbMATH Keywords: stable system of Hodge bundles
zbMATH Keywords: Hermitian-Yang-Mills connection
zbMATH Keywords: uniformized by a bounded symmetric domain
reviewed by: Michael K. Murray
MaRDI profile type: Publication
cites work: Infinite determinants, stable bundles and curvature
cites work: Stable and unitary vector bundles on a compact Riemann surface
cites work: Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
description: scientific article; zbMATH DE number 4034117