Albuquerque, Rui; Consiglieri, Luisa Invariant connections on Euclidean space. (English) Zbl 1219.32010 Bol. Soc. Parana. Mat. (3) 27, No. 1, 65-83 (2009). The equivalence problem for flat \(\mathcal{C}^1\) connections in Euclidean space is studied and solved in this article. The authors use methods from the theory of differential equations to find an affine transformation of \(\mathbb R^n\) taking the given flat connection to the so called trivial connection. Reviewer: Eugen Mihailescu (Bucureşti) MSC: 32S05 Local complex singularities 37D10 Invariant manifold theory for dynamical systems 53A15 Affine differential geometry 53B05 Linear and affine connections Keywords:linear connection; invariant connection; equivalence problem; orbifold; trivial connection; flat connection PDFBibTeX XMLCite \textit{R. Albuquerque} and \textit{L. Consiglieri}, Bol. Soc. Parana. Mat. (3) 27, No. 1, 65--83 (2009; Zbl 1219.32010) Full Text: DOI