Position Vectors of Curves With Recpect to Darboux Frame in the Galilean Space $G_3$

Tevfik Şahin; Buket Ceylan Dirişen

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arXiv · 1707.03930

Position Vectors of Curves With Recpect to Darboux Frame in the Galilean Space $G_3$

Tevfik Şahin·Buket Ceylan Dirişen

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Abstract

In this paper, we investigate the position vector of a curve on the surface in the Galilean 3-space G^3. Firstly, the position vector of a curve with respect to the Darboux frame is determined. Secondly, we obtain the standard representation of the position vector of the curve with respect to Darboux frame in terms of the geodesic, normal curvature and geodesic torsion. As a result of this, we define the position vectors of geodesic, asymptotic and normal line along with some special curves with respect to Darboux frame. Finally, we elaborate on some examples and provide their graphs.

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BibTeX RIS

Tevfik Şahin, Buket Ceylan Dirişen. 2017-07-12. Position Vectors of Curves With Recpect to Darboux Frame in the Galilean Space $G_3$. https://arxiv.org/abs/1707.03930

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