A Generalized Frame Bundle for Certain Fréchet Vector Bundles and Linear Connections

VASSILIOU, Efstathios; GALANIS, George

VASSILIOU, Efstathios ; GALANIS, George

Tokyo J. of Math., Tome 20 (1997) no. 2, p. 129-137 / Harvested from Project Euclid

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Résumé

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

$E_i$ .

Publié le : 1997-06-15
Classification:

@article{1270042405,
     author = {VASSILIOU, Efstathios and GALANIS, George},
     title = {A Generalized Frame Bundle for Certain Fr\'echet Vector Bundles and Linear Connections},
     journal = {Tokyo J. of Math.},
     volume = {20},
     number = {2},
     year = {1997},
     pages = { 129-137},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270042405}
}

VASSILIOU, Efstathios; GALANIS, George. A Generalized Frame Bundle for Certain Fréchet Vector Bundles and Linear Connections. Tokyo J. of Math., Tome 20 (1997) no. 2, pp.  129-137. http://gdmltest.u-ga.fr/item/1270042405/