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Invariant connections on Euclidean space. (English) Zbl 1219.32010

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.

MSC:

32S05 Local complex singularities
37D10 Invariant manifold theory for dynamical systems
53A15 Affine differential geometry
53B05 Linear and affine connections
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