Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection

Abstract

In this study, we present a problem that consists in flattening the curvature associated with an affine connection on ℝ2. This problem involves distributions and symmetric affine connections defined on a differential manifold M. For rank 1 constant distributions, we characterize the existence of solutions and get sufficient conditions to solve the problem. The general statement of the problem and some illustrative examples are given.