PLANE CURVES WITH SAME EQUI-AFFINE AND EUCLIDEAN INVARIANTS

Abstract

In the present paper, we consider and solve the problem of finding parametric plane curves with the same equi-affine and Frenet curvatures. We then classify the parametric plane curves with prescribed equi-affine curvature by solving certain ordinary differential equations. Our classification generalizes the plane curves with constant equi-affine curva-ture. Several examples are also given by figures. © 2021, Bayram Sahin. All rights reserved.