Universal connections in Fréchet principal bundles

George Galanis

doi:10.1007/s-10998-007-1001-z

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 54: Issue 1

Universal connections in Fréchet principal bundles

Author:

George Galanis

George Galanis Naval Academy of Greece Section of Mathematics Xatzikyriakion, Piraeus 185 39 Greece Xatzikyriakion, Piraeus 185 39 Greece

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Pages:: 1–13

Online Publication Date:: 25 Feb 2007

Publication Date:: 01 Mar 2007

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s-10998-007-1001-z

Keywords:: 58B25; 53C05; 58A05; Universal connections; Fréchet principal bundles; projective limits

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Abstract

A new methodology leading to the construction of a universal connection for Frchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Frchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector space, we endow the bundle J¹P of 1-jets of the sections of a Frchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)