Bundles with spherical Euler class.
type: Item
instance of: scholarly article
title: Bundles with spherical Euler class.
zbMATH Open document ID: 1065.53040
author: Luis Guijarro
author: Thomas Schick
author: Gerard Walschap
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: In this note, the authors show that the holonomy group of a Riemannian connection on a \(k\)-dimenional Euclidean vector bundle acts transitively on the unit sphere bundle whenever the Euler class is spherical. They give topological criteria when this actually happens and some rigidity consequences for complete, noncompact manifolds of nonnegative sectional curvature. The article is closely related to former work of the first and the last author [see \textit{L. Guijarro, G. Walschap}, Math. Z. 237, No. 2, 251--257 (2001; Zbl 0988.53023)].
reviewed by: Ilka Agricola
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 2101027
zbMATH Keywords: holonomy group
zbMATH Keywords: vector bundle
zbMATH Keywords: unit sphere bundle
zbMATH Keywords: Euler class
zbMATH Keywords: spherical
MaRDI profile type: Publication
full work available at URL: pjm.2002.207.377
OpenAlex ID: W1983952878
DOI: 10.2140/PJM.2002.207.377
description: scientific article; zbMATH DE number 2101027