A generalized frame bundle for certain Fréchet vector bundles and linear connections
type: Item
instance of: scholarly article
title: A generalized frame bundle for certain Fréchet vector bundles and linear connections
zbMATH Open document ID: 0894.58006
author: E. Vassiliou
author: George N. Galanis
published in: Tokyo Journal of Mathematics
publication date: 1998-09-07T00:00:00Z
review text: The authors consider a projective system of Banach vector bundles whose limit is a Fréchet bundle \(E\) of type fibre \(F\) and construct a generalized bundle of frames \(P(E)\) of \(E\) by revising entirely the classical notion and by substituting \(GL(F)\) with an appropriate enlarged structure group. It is proved that \(E\) is associated with \(P(E)\) and linear connections of \(E\) correspond to principal connections of \(P(E)\). For related work, see \textit{E. Vassiliou} [Period. Math. Hung. 13, 289-308 (1982; Zbl 0525.53044)] and \textit{T. Sakurai} and \textit{T. Nono} [Bull. Fukuoka Univ. Educ., Part III 30, 17-27 (1980; Zbl 0469.58001)].
Mathematics Subject Classification ID: 58B25
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 1054596
zbMATH Keywords: Fréchet vector bundles
zbMATH Keywords: frame bundle
zbMATH Keywords: linear connections
reviewed by: Maido Rahula
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042405
OpenAlex ID: W1967520026
DOI: 10.3836/TJM/1270042405
description: scientific article; zbMATH DE number 1054596