@article{article_877170, title={Associated curves of a Frenet curve in the dual Lorentzian space}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={71}, pages={285–304}, year={2022}, DOI={10.31801/cfsuasmas.877170}, author={Abalı, Bahar and Yücesan, Ahmet}, keywords={Dual Lorentzian space, associated curves, dual general helix, dual slant helix, principal directed rectifying curve, ruled surface}, abstract={In this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-ams-R" style="padding-top:.441em;padding-bottom:.316em;">D </span> </span> </span> </span> </span> <span class="mjx-stack" style="vertical-align:-.267em;"> <span class="mjx-sup" style="font-size:70.7%;padding-bottom:.255em;padding-left:0px;padding-right:.071em;"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">3 </span> </span> </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;padding-right:.071em;"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">1 </span> </span> </span> </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">D13 </span> </span>. We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in $\mathbb{D}^{2}$ or a hyperbola in $\mathbb{D}_{1}^{2}$ and the principal directed curve of a slant helix in $\mathbb{D}_{1}^{3}$ are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in $\mathbb{D}_{1}^{3}$, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-ams-R" style="padding-top:.441em;padding-bottom:.316em;">R </span> </span> </span> </span> </span> <span class="mjx-stack" style="vertical-align:-.267em;"> <span class="mjx-sup" style="font-size:70.7%;padding-bottom:.255em;padding-left:0px;padding-right:.071em;"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">3 </span> </span> </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;padding-right:.071em;"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">1 </span> </span> </span> </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">R13 </span> </span>.}, number={1}, publisher={Ankara University}