Plane curves with same equi-affine and Euclidean invariants

  • Muhittin Evren Aydın
  • Esra Erdem
  • Munevver Yıldırım Yılmaz Firat University
Keywords: Plane curve, Equiaffine transformation, Equiaffine curvature, Euclidean curvature.


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.