Plane curves with same equi-affine and Euclidean invariants

Abstract

In the present paper, we consider and solve the problem of finding plane curves with the same equi-affine and Frenet curvatures. We then classify the plane curves with prescribed equi-affine curvature by solving certain ordinary differential equations. Our classification generalizes the plane curves with constant equi-affine curvature. Several examples are also given by figures.