Original scientific paper

Characterizations of timelike slant helices in Minkowski 3-space

İsmail Gök ; Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey
Semra Kaya Nurkan ; Department of Mathematics, Faculty of Sciences and Arts, Usak University, Usak, Turkey
Kazim İlarslan ; Department of Mathematics, Faculty of Sciences and Arts, Kirikkale University,Kirikkale, Turkey
Levent Kula ; Department of Mathematics, Faculty of Sciences and Arts, Ahi Evran University, Kirsehir, Turkey
Mesut Altinok ; Department of Mathematics, Faculty of Sciences and Arts, Ahi Evran University, Kirsehir, Turkey

Abstract

In this paper, we investigate the tangent indicatrix, the principal normal indicatrix and the binormal indicatrix of a timelike curve in Minkowski $3$-space $\mathbb{E}_{1}^{3}$ and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize a timelike curve to be a slant helix by using the Frenet apparatus of a spherical indicatrix of the curve. Also, related examples and their illustrations are given.

Keywords

Minkowski 3-space; timelike curve; slant helix; general helix; spherical helix; the tangent indicatrix; the principal normal indicatrix; the binormal indicatrix

Hrčak ID:

121830

URI

https://hrcak.srce.hr/121830

Publication date:

26.5.2014.

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