Characterizations of Frenet curves in Galilean 3-space

Abstract

The aim of this paper is to prove that the distance function of every Frenet curve in G₃ satisfies a 4-th order differential equation. Also, we show that if α is a unit speed Frenet curve in G₃, then <α(s),T(s)>=s+c if and only if α is a rectifying curve. Finally, we obtain some characterizations of spherical curves and helices via the 4-th order differential equation (4).