On equiform Darboux helices in Galilean 3-space

Ufuk Öztürk; Esra Betül Koç Öztürk; Emilija Milojko Nešović

Vol. 23 No. 2 (2018)

Regular Articles

On equiform Darboux helices in Galilean 3-space

Published 2017-10-17

Ufuk Öztürk
Esra Betül Koç Öztürk
Emilija Milojko Nešović

Ufuk Öztürk
University of Cankiri Karatekin

Esra Betül Koç Öztürk
University of Cankiri Karatekin

Emilija Milojko Nešović
University of Kragujevac Faculty of Science

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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.

Keywords

equiform geometry, equiform Darboux vector, Galilean 3-space

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Author Biography

Ufuk Öztürk

Department of mathematics,

assistant professor

Esra Betül Koç Öztürk

Department of mathematics,

assistant professor

Emilija Milojko Nešović

Department of mathematics and informatics,

associate professor