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On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$

Year 2022, Issue: 40, 54 - 59, 30.09.2022
https://doi.org/10.53570/jnt.1148933

Abstract

This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame in 3-dimensional Euclidean space ($\mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves with modified orthogonal frames in $\mathbb{E}^{3}$.

References

  • M. Barros, General Helices and a Theorem of Lancret, Proceedings of the American Mathematical Society 125 (5) (1997), 1503–1509.
  • D. J. Struik, Lectures on Classical Differential Geometry, Addison Wesley, 1988.
  • S. Izumiya, N. Takeuchi, New Special Curves and Developable Surfaces, Turkish Journal of Mathematics 28 (2) (2004), 153–164.
  • T. Y. Shaker, Evolution of Space Curves Using Type-3 Bishop Frame, Caspian Journal of Mathematical Sciences (CJMS) 8 (1) (2019), 58–73.
  • M. Bektaş, M. Y. Yılmaz, (k,m)-Type Slant Helices for Partially Null and Pseudo-Null Curves in Minkowski Space, Applied Mathematics and Nonlinear Sciences 5(1) (2020) 515–520.
  • M. Y. Yilmaz, M. Bektaş, Slant Helices of (k, m)-Type in E^4, Acta Universitatis Sapientiae, Mathematica 10 (2) (2018) 395–401.
  • F. Bulut, M. Bektaş, Special Helices on Equiform Differential Geometry of Spacelike Curves in Minkowski Spacetime, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2) (2020) 1045–1056.
  • B. Bükcü, M. K. Karacan, Spherical Curves with Modified Orthogonal Frame, Journal of New Results in Science 5 (10) (2016) 60–68.
  • K. Eren, H. H. Kosal, Evolution of Space Curves and the Special Ruled Surfaces with Modified Orthogonal Frame, American Institute of Mathematical Sciences-Aims.
  • A. Z. Azak, Involute-Evolute Curves according to Modified Orthogonal Frame, Journal of Science and Arts 21 (2) (2021) 385–394.
  • M. S. Lone, H. Es, M. K. Karacan, B. Bükcü, On Some Curves with Modified Orthogonal Frame in Euclidean 3-Space, Iranian Journal of Science and Technology, Transactions A: Science 43 (4) (2019) 1905–1916.
  • N. Ekmekci, On General Helices and Submanifolds of an Indefinite-Riemannian Manifold, Analele Stiintifice Universitati Ale I Cuza Lasi Matematica (NS) 46 (2001) 263–270.
  • T. Ahmad, A. R. Lopez, Slant Helices in Minkowski Space E_1^3, Journal of the Korean Mathematical Society 48 (1) (2011) 159–167.
  • S. Kumar, B. Pal, K-Type Slant Helices on Spacelike and Timelike Surfaces, Acta et Commentationes Universitatis Tartuensis de Mathematica 25 (2) (2021) 201–220.
Year 2022, Issue: 40, 54 - 59, 30.09.2022
https://doi.org/10.53570/jnt.1148933

Abstract

References

  • M. Barros, General Helices and a Theorem of Lancret, Proceedings of the American Mathematical Society 125 (5) (1997), 1503–1509.
  • D. J. Struik, Lectures on Classical Differential Geometry, Addison Wesley, 1988.
  • S. Izumiya, N. Takeuchi, New Special Curves and Developable Surfaces, Turkish Journal of Mathematics 28 (2) (2004), 153–164.
  • T. Y. Shaker, Evolution of Space Curves Using Type-3 Bishop Frame, Caspian Journal of Mathematical Sciences (CJMS) 8 (1) (2019), 58–73.
  • M. Bektaş, M. Y. Yılmaz, (k,m)-Type Slant Helices for Partially Null and Pseudo-Null Curves in Minkowski Space, Applied Mathematics and Nonlinear Sciences 5(1) (2020) 515–520.
  • M. Y. Yilmaz, M. Bektaş, Slant Helices of (k, m)-Type in E^4, Acta Universitatis Sapientiae, Mathematica 10 (2) (2018) 395–401.
  • F. Bulut, M. Bektaş, Special Helices on Equiform Differential Geometry of Spacelike Curves in Minkowski Spacetime, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2) (2020) 1045–1056.
  • B. Bükcü, M. K. Karacan, Spherical Curves with Modified Orthogonal Frame, Journal of New Results in Science 5 (10) (2016) 60–68.
  • K. Eren, H. H. Kosal, Evolution of Space Curves and the Special Ruled Surfaces with Modified Orthogonal Frame, American Institute of Mathematical Sciences-Aims.
  • A. Z. Azak, Involute-Evolute Curves according to Modified Orthogonal Frame, Journal of Science and Arts 21 (2) (2021) 385–394.
  • M. S. Lone, H. Es, M. K. Karacan, B. Bükcü, On Some Curves with Modified Orthogonal Frame in Euclidean 3-Space, Iranian Journal of Science and Technology, Transactions A: Science 43 (4) (2019) 1905–1916.
  • N. Ekmekci, On General Helices and Submanifolds of an Indefinite-Riemannian Manifold, Analele Stiintifice Universitati Ale I Cuza Lasi Matematica (NS) 46 (2001) 263–270.
  • T. Ahmad, A. R. Lopez, Slant Helices in Minkowski Space E_1^3, Journal of the Korean Mathematical Society 48 (1) (2011) 159–167.
  • S. Kumar, B. Pal, K-Type Slant Helices on Spacelike and Timelike Surfaces, Acta et Commentationes Universitatis Tartuensis de Mathematica 25 (2) (2021) 201–220.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şeyda Özel 0000-0002-1519-2418

Mehmet Bektaş This is me 0000-0002-5797-4944

Publication Date September 30, 2022
Submission Date July 26, 2022
Published in Issue Year 2022 Issue: 40

Cite

APA Özel, Ş., & Bektaş, M. (2022). On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$. Journal of New Theory(40), 54-59. https://doi.org/10.53570/jnt.1148933
AMA Özel Ş, Bektaş M. On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$. JNT. September 2022;(40):54-59. doi:10.53570/jnt.1148933
Chicago Özel, Şeyda, and Mehmet Bektaş. “On the Characterisations of Curves With Modified Orthogonal Frame in $\mathbb{E}^{3}$”. Journal of New Theory, no. 40 (September 2022): 54-59. https://doi.org/10.53570/jnt.1148933.
EndNote Özel Ş, Bektaş M (September 1, 2022) On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$. Journal of New Theory 40 54–59.
IEEE Ş. Özel and M. Bektaş, “On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$”, JNT, no. 40, pp. 54–59, September 2022, doi: 10.53570/jnt.1148933.
ISNAD Özel, Şeyda - Bektaş, Mehmet. “On the Characterisations of Curves With Modified Orthogonal Frame in $\mathbb{E}^{3}$”. Journal of New Theory 40 (September 2022), 54-59. https://doi.org/10.53570/jnt.1148933.
JAMA Özel Ş, Bektaş M. On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$. JNT. 2022;:54–59.
MLA Özel, Şeyda and Mehmet Bektaş. “On the Characterisations of Curves With Modified Orthogonal Frame in $\mathbb{E}^{3}$”. Journal of New Theory, no. 40, 2022, pp. 54-59, doi:10.53570/jnt.1148933.
Vancouver Özel Ş, Bektaş M. On the Characterisations of Curves with Modified Orthogonal Frame in $\mathbb{E}^{3}$. JNT. 2022(40):54-9.


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