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June 1997 A Generalized Frame Bundle for Certain Fréchet Vector Bundles and Linear Connections
George GALANIS, Efstathios VASSILIOU
Tokyo J. Math. 20(1): 129-137 (June 1997). DOI: 10.3836/tjm/1270042405

Abstract

Let $(E_i)_{i\in\mathbf{N}}$ be a projective system of Banach vector bundles whose limit is a Fréchet bundle of fibre type $\mathbf{F}$. We construct a generalized bundle of frames $\mathbf{P}(E)$ of $E$ by revising entirely the classical notion and by substituting $GL(\mathbf{F})$ with an appropriate enlarged structure group. This is imposed by the pathology of $GL(\mathbf{F})$, which renders meaningless the ordinary frame bundle. As a result, we prove that $E$ is associated with $\mathbf{P}(E)$ and linear connections of $E$ correspond to (principal) connections of $\mathbf{P}(E)$. In particular, the former are necessarily projective limits of connections on the bundles $E_i$.

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George GALANIS. Efstathios VASSILIOU. "A Generalized Frame Bundle for Certain Fréchet Vector Bundles and Linear Connections." Tokyo J. Math. 20 (1) 129 - 137, June 1997. https://doi.org/10.3836/tjm/1270042405

Information

Published: June 1997
First available in Project Euclid: 31 March 2010

zbMATH: 0894.58006
MathSciNet: MR1451865
Digital Object Identifier: 10.3836/tjm/1270042405

Rights: Copyright © 1997 Publication Committee for the Tokyo Journal of Mathematics

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Vol.20 • No. 1 • June 1997
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