$D_{i}-$Darboux Slant Helices on Surface
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.
Keywords
Do-Darboux slant helix Dn-Darboux slant helix Dr-Darboux slant helix helix isophote curve relatively normal-slant helix
References
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- 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.
- 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.
- Babaarslan, M., Yayli, Y., On helices and Bertrand curves in Euclidean 3-space, Mathematical and Computational Applications, 18(1)(2013), 1–11.
- Barros, M., General helices and a theorem of Lancret, Proc Amer Math Soc., 125(5)(1997), 1503–1509.
- Doğan, F., Yaylı Y., On isophote curves and their characterizations, Turk J. Math., 39(2015), 650–664.
- Hananoi, S., Ito, N., Izumiya, S., Spherical Darboux images of curves on surfaces, Beitr Algebra Geom., 56(2015), 575–585.
- Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turk J. Math., 28(2004), 153–163.
- Kula, L., Yaylı, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1)(2005), 600–607.
- 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.
- Önder, M., Helices associated to helical curves, relatively normal-slant helices and isophote curves, arXiv preprint arXiv:2201.09684., (2022).
- 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).
- 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.
Abstract
References
- Ali, A.T., Position vectors of slant helices in Euclidean space E3, J. Egyptian Math. Soc., 20(2012) 1–6.
- 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.
- 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.
- Babaarslan, M., Yayli, Y., On helices and Bertrand curves in Euclidean 3-space, Mathematical and Computational Applications, 18(1)(2013), 1–11.
- Barros, M., General helices and a theorem of Lancret, Proc Amer Math Soc., 125(5)(1997), 1503–1509.
- Doğan, F., Yaylı Y., On isophote curves and their characterizations, Turk J. Math., 39(2015), 650–664.
- Hananoi, S., Ito, N., Izumiya, S., Spherical Darboux images of curves on surfaces, Beitr Algebra Geom., 56(2015), 575–585.
- Izumiya, S., Takeuchi, N., New special curves and developable surfaces, Turk J. Math., 28(2004), 153–163.
- Kula, L., Yaylı, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1)(2005), 600–607.
- 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.
- Önder, M., Helices associated to helical curves, relatively normal-slant helices and isophote curves, arXiv preprint arXiv:2201.09684., (2022).
- 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).
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 31, 2024 |
| Published in Issue | Year 2024 Volume: 16 Issue: 2 |