Research Article
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Year 2023, , 715 - 726, 29.10.2023
https://doi.org/10.36890/iejg.1362590

Abstract

References

  • [1] Doğan, F., Yaylı, Y.: On isophote curves and their characterizations. Turkish Journal of Mathematics, 39, 650–664 (2015). https://doi.org/10.3906/mat-1410-4
  • [2] Düldül, M., Macit, N.: Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe Journal of Mathematics and Statistics, 46, 397–408 (2017).
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Approximations of Parallel Surfaces Along Curves

Year 2023, , 715 - 726, 29.10.2023
https://doi.org/10.36890/iejg.1362590

Abstract

In this paper, we study developable surfaces which are flat and normal approximation of parallel surfaces along curves associated with three special vector fields. It is known that a surface whose points are at a constant distance along the normal of the surface is called a parallel surface. We investigate singularities of such developable surfaces. We show that under what conditions the approach surfaces are parallel. Also, we show that the approach surfaces are constant angle ruled surfaces if the curves selected on the surfaces are isophote, relatively normal-slant helix and helix.

References

  • [1] Doğan, F., Yaylı, Y.: On isophote curves and their characterizations. Turkish Journal of Mathematics, 39, 650–664 (2015). https://doi.org/10.3906/mat-1410-4
  • [2] Düldül, M., Macit, N.: Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe Journal of Mathematics and Statistics, 46, 397–408 (2017).
  • [3] Hananoi, S., Ito, N., Izumiya, S.: Spherical Darboux images of curves on surfaces. Beitr. Algebra Geom., 56, 575–585 (2015). https://doi.org/10.1007/s13366-015-0240-z
  • [4] Hananoi, S., Izumiya, S.: Normal developable surfaces of surfaces along curves. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 147, 177–203 (2017). https://doi.org/10.1017/S030821051600007X
  • [5] Izumiya, S., Otani, S.: Flat Approximations of Surfaces Along Curves. Demonstratio Mathematica, 48, 217–241 (2015). https://doi.org/10.1515/dema-2015-0018
  • [6] Kızıltuğ, S., Tarakcı, Ö., Yaylı, Y.: On the curves lying on parallel surfaces in the Euclidean 3-space E3. Journal of Advanced Research in Dynamical and Control Systems, 5, 26–35 (2013).
  • [7] Özkaldı, S., Yaylı, Y.: Constant Angle Surfaces and Curves in E3. International Electronic Journal of Geometry, 4, 70–78 (2011).
  • [8] Sabuncuoğlu, A.: Diferensiyel Geometri. Nobel Akademik Yayıncılık. Ankara (2016).
There are 8 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Büşra Köse 0009-0005-1739-4207

Yusuf Yaylı 0000-0003-4398-3855

Early Pub Date October 29, 2023
Publication Date October 29, 2023
Acceptance Date October 29, 2023
Published in Issue Year 2023

Cite

APA Köse, B., & Yaylı, Y. (2023). Approximations of Parallel Surfaces Along Curves. International Electronic Journal of Geometry, 16(2), 715-726. https://doi.org/10.36890/iejg.1362590
AMA Köse B, Yaylı Y. Approximations of Parallel Surfaces Along Curves. Int. Electron. J. Geom. October 2023;16(2):715-726. doi:10.36890/iejg.1362590
Chicago Köse, Büşra, and Yusuf Yaylı. “Approximations of Parallel Surfaces Along Curves”. International Electronic Journal of Geometry 16, no. 2 (October 2023): 715-26. https://doi.org/10.36890/iejg.1362590.
EndNote Köse B, Yaylı Y (October 1, 2023) Approximations of Parallel Surfaces Along Curves. International Electronic Journal of Geometry 16 2 715–726.
IEEE B. Köse and Y. Yaylı, “Approximations of Parallel Surfaces Along Curves”, Int. Electron. J. Geom., vol. 16, no. 2, pp. 715–726, 2023, doi: 10.36890/iejg.1362590.
ISNAD Köse, Büşra - Yaylı, Yusuf. “Approximations of Parallel Surfaces Along Curves”. International Electronic Journal of Geometry 16/2 (October 2023), 715-726. https://doi.org/10.36890/iejg.1362590.
JAMA Köse B, Yaylı Y. Approximations of Parallel Surfaces Along Curves. Int. Electron. J. Geom. 2023;16:715–726.
MLA Köse, Büşra and Yusuf Yaylı. “Approximations of Parallel Surfaces Along Curves”. International Electronic Journal of Geometry, vol. 16, no. 2, 2023, pp. 715-26, doi:10.36890/iejg.1362590.
Vancouver Köse B, Yaylı Y. Approximations of Parallel Surfaces Along Curves. Int. Electron. J. Geom. 2023;16(2):715-26.