Original scientific paper

On eqiform Darboux helices in Galilean 3-space

Ufuk Öztürk orcid.org/0000-0002-8800-7869 ; Department of Mathematics, University of Çankırı Karatekin, Çankırı, Turkey
Esra Betül Koç Öztürk orcid.org/0000-0002-9437-3443 ; A. H. R. Mah. Çayyolu Cad. Ada Sitesi, Çankırı, Turkey
Emilija Milojko Nešović orcid.org/0000-0003-3600-0486 ; Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Kragujevac, Serbia

Abstract

In this paper, we define equiform Darboux helices in a Galilean space \(G_{3}\) and obtain their explicit parameter equations. We show that equiform Darboux helices have only a 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 α is an equiform Darboux helix if an admissible curve \(\alpha\) is a rectifying curve. We also prove that there are no equiform curves of constant precession
and give some examples of equiform Darboux helices.

Keywords

Galilean 3-space; equiform geometry; Darboux vector

Hrčak ID:

198605

URI

https://hrcak.srce.hr/198605

Publication date:

7.11.2018.

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