Transformations of linear connections. II
type: Item
instance of: scholarly article
title: Transformations of linear connections. II
zbMATH Open document ID: 0617.58003
DOI: 10.1007/BF01848223
author: Yanyan Li
published in: Periodica Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: This paper is a continuation of the previous paper by the author [ibid. 13, 289-308 (1982; Zbl 0525.53044)] in which connections defined on Banachable fibre bundles were considered. Now, the author elucidates that paper with two applications. In the first, he views linear connections as systems of differential equations. Specializing this to the case of trivial bundles over \(S^ 1\), connections correspond to equations with periodic coefficients. Hence, applying the theory of Floquet, the author obtains a Floquet-type theorem for infinite-dimensional connections on such bundles. In the second example, he proves that the canonical connections of parallelizable manifolds are naturally derived from the canonical flat connection of appropriate trivial bundles.
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 4001019
zbMATH Keywords: linear connections on Banach vector bundles
zbMATH Keywords: connections on parallelizable manifolds
zbMATH Keywords: Banach-Lie groups
reviewed by: Jan Kubarski
MaRDI profile type: Publication
cites work: Q5341449
cites work: Liesche Gruppen und affin zusammenhängende Mannigfaltigkeiten
cites work: Q3897665
cites work: Lie groups with Banach spaces as parameter spaces
cites work: Q5654428
cites work: On Floquet’s theorem in Hilbert spaces
cites work: Transformations of linear connections
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description: scientific article; zbMATH DE number 4001019