Cohomology and splitting of Hermitian-Einstein vector bundles
type: Item
instance of: scholarly article
title: Cohomology and splitting of Hermitian-Einstein vector bundles
zbMATH Open document ID: 0729.32013
DOI: 10.1007/BF01446589
author: Bernard Shiffman
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164798
review text: Using a cohomology vanishing theorem the following result is proved. Let E be a Hermitian-Einstein vector bundle of rank r on \({\mathbb{C}}{\mathbb{P}}^ n\) and let \(I=\{R(e,\bar e,t,\bar t):\) \(e\in E_ x\), \(t\in T_ x\), \(| e| =| t| =1\), \(x\in {\mathbb{C}}{\mathbb{P}}^ n\}\), where R is the curvature tensor. If \(n\geq r^ 2+1\) and \[ \sup I-\inf I<(n-r^ 2)/r^ 2(r^ 2+1), \] then E splits, i.e. E(\(\mu\)) is trivial for some integer \(\mu\).
Mathematics Subject Classification ID: 32Q20
Mathematics Subject Classification ID: 32L20
zbMATH DE Number: 4204794
zbMATH Keywords: splitting
zbMATH Keywords: cohomology vanishing theorem
zbMATH Keywords: Hermitian-Einstein vector bundle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4204794