Characterizations of timelike slant helices in Minkowski 3-space

İsmail Gök, Semra Kaya Nurkan, Kazim İlarslan, Levent Kula, Mesut Altinok


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.


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

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ISSN: 1331-0623 (Print), 1848-8013 (Online)