On equiform Darboux helices in Galilean 3-space

Abstract

In this paper, we define   equiformDarboux helices in Galilean space $\mathbb{G}_{3}$  and  obtain their explicit parameter equations. We show that equiform Darboux helices have only non-isotropic axis and   characterize equiform Darboux vectors of  equiform Darboux helices in terms of equiform rectifying curves.  We prove that an equiform Darboux vector of  an equiform Darboux helix $\alpha$ is an equiform Darboux helix, if an admissible curve $\alpha$ is a rectifying curve. We also prove that there are no equiform curves of the constant precession and give some examples of the equiform Darboux helices.