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Journals / Turkish Journal of Mathematics and Computer Science / 2024 / Volume: 16 Issue: 2

$D_{i}-$Darboux Slant Helices on Surface

Akın Alkan(MANİSA CELÂL BAYAR ÜNİVERSİTESİ, GÖRDES MESLEK YÜKSEKOKULU)0000-0002-8179-9525
Hüseyin Kocayiğit(MANISA CELAL BAYAR UNIVERSITY)0000-0001-6503-8243
Tuba Ağırman Aydın(BAYBURT UNIVERSITY, BAYBURT FACULTY OF EDUCATION)0000-0001-8034-0723
Pages
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Publication Date
2024-12-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Moreover, the position vectors of the $D_{i}$-Darboux slant helices are obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we consider $D_{i}$-Darboux slant helices which are new surface curves on an oriented surface.
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Key Findings & Data:We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the $D_{i}$-Darboux slant helices.
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Conclusion & Impact:Moreover, the position vectors of the $D_{i}$-Darboux slant helices are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Do-Darboux slant helix · Dn-Darboux slant helix · Dr-Darboux slant helix

Abstract

In this study, we consider $D_{i}$-Darboux slant helices which are new surface curves on an oriented surface. We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the $D_{i}$-Darboux slant helices. Moreover, the position vectors of the $D_{i}$-Darboux slant helices are obtained.

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Cite This Article

Alkan, A., Kocayiğit, H., Aydın, T. A. (2024). $D_{i}-$Darboux Slant Helices on Surface. Turkish Journal of Mathematics and Computer Science, Volume: 16 Issue: 2. https://doi.org/10.47000/tjmcs.1310722

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References (13)

  1. Ali, A.T., Position vectors of slant helices in Euclidean space E3, J. Egyptian Math. Soc., 20(2012) 1–6.
  2. Alkan, A., Kocayiğit, H., Ağırman Aydın, T., New moving frames for the curves lying on a surface, Sigma Journal of Engineering and Natural Sciences, 42(4)(2024), 2023–2029.
  3. Babaarslan, M., Tandogan, Y.A., Yayli, Y., A note on Bertrand curves and constant slope surfaces according to Darboux frame, Journal of Advanced Mathematical Studies, 5(1)(2012), 87–97.
  4. Babaarslan, M., Yayli, Y., On helices and Bertrand curves in Euclidean 3-space, Mathematical and Computational Applications, 18(1)(2013), 1–11.
  5. Barros, M., General helices and a theorem of Lancret, Proc Amer Math Soc., 125(5)(1997), 1503–1509.
  6. Doğan, F., Yaylı Y., On isophote curves and their characterizations, Turk J. Math., 39(2015), 650–664.
  7. Hananoi, S., Ito, N., Izumiya, S., Spherical Darboux images of curves on surfaces, Beitr Algebra Geom., 56(2015), 575–585.
  8. Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turk J. Math., 28(2004), 153–163.
  9. Kula, L., Yaylı, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1)(2005), 600–607.
  10. Macit, N., Düldül, M., Relatively normal-slant helices lying on a surface and their characterizations, Hacettepe Journal of Mathematics and Statistics, 46(3)(2017), 397–408.
  11. Önder, M., Helices associated to helical curves, relatively normal-slant helices and isophote curves, arXiv preprint arXiv:2201.09684., (2022).
  12. Puig-Pey, J., G´alvez, A., Iglesias, A., Helical curves on surfaces for computer-aided geometric design and manufacturing, in: Computational Science and Its Applications-ICCSA Part II, 771-778. in: Lecture Notes in Comput Sci Vol. 3044, Springer, Berlin, (2004).
  13. Zıplar, E., Şenol, A., Yaylı, Y., On Darboux helices in Euclidean 3-space, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12(3)(2012), 73–80.