Singularities of invariant connections
type: Item
instance of: scholarly article
title: Singularities of invariant connections
zbMATH Open document ID: 0782.53059
DOI: 10.1007/BF02418211
author: A. M. Amores
author: Manuel Gutiérrez
published in: General Relativity and Gravitation
publication date: 1993-05-16T00:00:00Z
review text: The authors study Schmidt's \(b\)-boundary construction [\textit{B. Schmidt}, Gen. Relativ. Gravitation 1, 269-280 (1971; Zbl 0332.53039)] for homogeneous spaces \(P/G\) with an invariant connection (\(P\) is here a Lie group, \(G\) a closed subgroup). If the connection on \(P/G\) is the reduction of an invariant connection on \(P/G\) then there are no \(b\)- incomplete inextensible curves. In the general case the authors provide examples of \(b\)-incomplete, inextensible curves and also show that different curves may have the same \(b\)-boundary point as a limit in \(\overline{P/G}\). They generalize previous work of \textit{C. T. J. Dodson} and \textit{L. J. Sulley} [Lett. Math. Phys. 1, 301 (1977)].
reviewed by: Marcus Kriele
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 83C75
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 167656
zbMATH Keywords: \(b\)-boundary
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: invariant connection
zbMATH Keywords: Lie group
zbMATH Keywords: connection
zbMATH Keywords: reduction
zbMATH Keywords: \(b\)-incomplete
MaRDI profile type: Publication
cites work: On the b-completion of certain quotient spaces
cites work: Space-time edge geometry
cites work: The \(b\)-boundary of \(S^1\) with a constant connection
cites work: The Large Scale Structure of Space-Time
cites work: A new definition of singular points in general relativity
full work available at URL: https://doi.org/10.1007/bf02418211
OpenAlex ID: W1990515034
description: scientific article; zbMATH DE number 167656