Invariant connections on Euclidean space

abstract: We recall and solve the equivalence problem for a ﬂat C connection ∇ in Euclidean space, with methods from the theory of diﬀerential equations. The problem consists in ﬁnding an aﬃne transformation of R^n taking ∇ to the so called trivial connection. Generalized solutions are found in dime...

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Bibliographic Details
Main Authors:	Luisa Consiglieri, Rui Albuquerque
Format:	Article
Language:	English
Published:	Sociedade Brasileira de Matemática 2009-07-01
Series:	Boletim da Sociedade Paranaense de Matemática
Subjects:	linear connection invariant connection equivalence problem orbifold.
Online Access:	http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9069/5273

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spelling	doaj-8bcb56000c454be68cb158be547abb1a2020-11-24T22:45:24ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882009-07-012716582Invariant connections on Euclidean spaceLuisa ConsiglieriRui Albuquerqueabstract: We recall and solve the equivalence problem for a ﬂat C connection ∇ in Euclidean space, with methods from the theory of diﬀerential equations. The problem consists in ﬁnding an aﬃne transformation of R^n taking ∇ to the so called trivial connection. Generalized solutions are found in dimension 1 and some exam-ple problems are solved in dimension 2, mainly dealing with ﬂat connections. A description of invariant connections in the plane is attempted, in view the study of real orbifolds. Complex meromorphic connections are shown in the cone cL(p,q) of a lens-space.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9069/5273linear connectioninvariant connectionequivalence problemorbifold.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Luisa Consiglieri Rui Albuquerque
spellingShingle	Luisa Consiglieri Rui Albuquerque Invariant connections on Euclidean space Boletim da Sociedade Paranaense de Matemática linear connection invariant connection equivalence problem orbifold.
author_facet	Luisa Consiglieri Rui Albuquerque
author_sort	Luisa Consiglieri
title	Invariant connections on Euclidean space
title_short	Invariant connections on Euclidean space
title_full	Invariant connections on Euclidean space
title_fullStr	Invariant connections on Euclidean space
title_full_unstemmed	Invariant connections on Euclidean space
title_sort	invariant connections on euclidean space
publisher	Sociedade Brasileira de Matemática
series	Boletim da Sociedade Paranaense de Matemática
issn	0037-8712 2175-1188
publishDate	2009-07-01
description	abstract: We recall and solve the equivalence problem for a ﬂat C connection ∇ in Euclidean space, with methods from the theory of diﬀerential equations. The problem consists in ﬁnding an aﬃne transformation of R^n taking ∇ to the so called trivial connection. Generalized solutions are found in dimension 1 and some exam-ple problems are solved in dimension 2, mainly dealing with ﬂat connections. A description of invariant connections in the plane is attempted, in view the study of real orbifolds. Complex meromorphic connections are shown in the cone cL(p,q) of a lens-space.
topic	linear connection invariant connection equivalence problem orbifold.
url	http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9069/5273
work_keys_str_mv	AT luisaconsiglieri invariantconnectionsoneuclideanspace AT ruialbuquerque invariantconnectionsoneuclideanspace
_version_	1725688738950938624

Invariant connections on Euclidean space

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