Invariant connections on Euclidean space

Abstract

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.

Keywords

• linear connection
• invariant connection
• equivalence problem
• orbifold.