Connection metrics of nonnegative curvature on vector bundles
type: Item
instance of: scholarly article
title: Connection metrics of nonnegative curvature on vector bundles
zbMATH Open document ID: 0695.53032
DOI: 10.1007/BF02568500
author: Martin Strake
author: Gerard Walschap
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155476
review text: Let \(R^ k\to E\to^{\pi}M\) be a Euclidean vector bundle with Riemannian connection \(\nabla\) over a compact manifold M of positive sectional curvature. It is proved that if \(\nabla\) is radially symmetric, then E admits a complete metric g of nonnegative sectional curvature. Although radial symmetry is not necessary, a differential inequality is given which must be satisfied by the curvature tensor \(R^{\nabla}\) if (E,g) is nonnegatively curved. It is shown that a slightly sharper inequality is actually sufficient if \(k=2\), or \(R^{\nabla}\) is sufficiently nontrivial.
reviewed by: Lajos Tamássy
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 4138698
zbMATH Keywords: Euclidean vector bundle
zbMATH Keywords: Riemannian connection
zbMATH Keywords: positive sectional curvature
zbMATH Keywords: complete metric
MaRDI profile type: Publication
cites work: Q4720334
cites work: Q3261425
cites work: Q3730551
cites work: Q5825483
cites work: \(\Sigma\)-flat manifolds and Riemannian submersions
cites work: Totally geodesic maps
cites work: Nonnegatively curved manifolds with souls of codimension 2
description: scientific article; zbMATH DE number 4138698