Connections on \(\mathbb{A}\)-frame bundles
type: Item
instance of: scholarly article
zbMATH Open document ID: 1021.58004
publication date: 2003-10-12T00:00:00Z
Mathematics Subject Classification ID: 58A40
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 18F15
zbMATH DE Number: 1688864
zbMATH Keywords: \(\mathbb{A}\)-bundles
zbMATH Keywords: frame bundles
zbMATH Keywords: connections
MaRDI profile type: Publication
author: Evangelos E. Vassiliou
author: M. H. Papatriantafillou
title: Connections on \(\mathbb{A}\)-frame bundles
published in: Scientiae Mathematicae Japonicae
review text: Let \(\mathbb{A}\) be a topological algebra. The author studies relations between \(\mathbb{A}\)-connections on \(\mathbb{A}\)-bundles \(\ell\) and connections on the frame bundle \(F(\ell)\). Namely, if \(\mathbb{A}\) is a \(Q\)-algebra, then \(\mathbb{A}\)-connections on \(\ell\) correspond bijectively to connections on \(F(\ell)\). If \(\mathbb{A}\) is not a \(Q\)-algebra then \(F(\ell)\) is only a topological principal bundle and \(\mathbb{A}\)-connections on \(\ell\) correspond bijectively to sheaf-theoretic objects which can be called connections on the sheaf of germs of sections on \(F(\ell)\).
reviewed by: Josef Janyška
description: scientific article; zbMATH DE number 1688864