2017•arXiv (Cornell University)Open access

Special Smarandache Curves with Respect to Darboux Frame in the Galilean 3-Space

Tevfik Şahin, Merve Okur

Abstract

In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3. Furthermore, we give general position vectors of special Smarandache curves of geodesic, asymptotic and curvature line on the surface in G3. As a result of this, we provide some related examples of these curves.

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Key concepts: Frenet–Serret formulas, Galilean, Ruled surface, Curvature, Mathematics, Geodesic, Mathematical analysis, Space (punctuation)