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

Yıl 2022, Sayı: 40, 54 - 59, 30.09.2022

Şeyda Özel , Mehmet Bektaş

https://doi.org/10.53570/jnt.1148933

Öz

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 $\mathbb{E}^{3}$.

Anahtar Kelimeler

helices, (k,m)-form Slant Helices, modified orthogonal frame

Kaynakça

• 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.