We recall and solve the equivalence problem for a flat C^1 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 example 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.
@article{9069,
title = {Invariant connections on Euclidean space - doi: 10.5269/bspm.v27i1.9069},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v27i1.9069},
language = {EN},
url = {http://dml.mathdoc.fr/item/9069}
}
Albuquerque, Rui; Consiglieri, Luisa. Invariant connections on Euclidean space - doi: 10.5269/bspm.v27i1.9069. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v27i1.9069. http://gdmltest.u-ga.fr/item/9069/