Journals / Turkish Journal of Science and Technology / 2026 / Volume: 16 Issue: 1

The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24

M3 (δ0)⊂E2 4 9 3-Uzayında non-Dejenere Eğriler Tarafından Elde Edilen Helis ve Slant Helisler

Fatma Almaz(Fırat Üniversitesi)0000-0002-1060-7813
Mihriban Külahci(FIRAT ÜNİVERSİTESİ)0000-0002-8621-5779
Pages
—
Publication Date
2021-03-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, in M3(δ0) 3-space the necessary and sufficient conditions for the non-degenerate curves to be slant helix are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate helix and slant helices using non-degenerate curves in term of Sabban frame in de Sitter 3-space or Anti de Sitter 3-space M3(δ0).
📊
Key Findings & Data:In this paper, we investigate helix and slant helices using non-degenerate curves in term of Sabban frame in de Sitter 3-space or Anti de Sitter 3-space M3(δ0).
💡
Conclusion & Impact:Furthermore, in M3(δ0) 3-space the necessary and sufficient conditions for the non-degenerate curves to be slant helix are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sabban frame · helix · slant helix

Abstract

In this paper, we investigate helix and slant helices using non-degenerate curves in term of Sabban frame in de Sitter 3-space or Anti de Sitter 3-space M3(δ0). Furthermore, in M3(δ0) 3-space the necessary and sufficient conditions for the non-degenerate curves to be slant helix are given.

🔖

Cite This Article

Almaz, F., Külahci, M. (2021). The Helix and Slant Helices Generated by non-Degenerate Curves in M3(δ0)⊂E24. Turkish Journal of Science and Technology, Volume: 16 Issue: 1. https://ajindex.com/articles/1557853

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. Ali AT, Lopez R. Timelike B2-Slant Helices in Minkowski Space E14. Archıvum Mathematicum(BRNO) Tomus, 2010; 46: 39-46.
  2. Ali AT. Position vectors of spacelike general helices in Minkowski 3-Space. Nonlinear Analysis 2010; 73: 1118-1126.
  3. Ali AT, Lopez R, Turgut M. k-type partially null and pseudo null slant helices in Minkowski 4-Space. Math. Commun. 2012; 17: 93-103.
  4. Ali AT, Turgut M. Some Characterizations of slant helices in the Euclidean En. arXiv: 0904.1187v1 2009; 8pp.
  5. Barros M, Ferrandes A, Lukas P, Mero.no MA. General helices in the three dimensional Lorentzian space forms. Rocky Mountain J. Math 2001; 31(2): 373-388.
  6. Camci C, Ilarslan K, Kula L, Hacisalihoglu HH. Harmonic curvatures and generalized helices in En. Chaos, Solitons and Fractals 2009; 40: 2590-2596.
  7. Ferrandez A, Gimenez A, Lucas P. Null generalized helices in Lorentz-Minkowski Spaces. Journal of Physics A: Math. and General 2002; 35(39): 8243-8251.
  8. Gluck H. Higher curvature of curves in Euclidean space. Amer. Math. Monthly 1996; 73: 699-704.
  9. Izumiya S, Takeuchi N. New special curves and devalopable surface. Turk J. Math. 2004; 28: 153-163.
  10. Ilarslan K, Boyacioglu O. Position vectors of a timelike and a null helix in Minkowski 3-Space. Chaos Solitons and Fractals 2008; 38: 1383-1389.
  11. Kula L, Yayli Y, On slant helix and its spherical indicatrix. App. Math. and Computation 2005; 169: 600-607.
  12. Kulahci M, Bektaş M, Ergüt M. Curves of AW(k)-type in 3-dimensional null cone. Physics Letters A371 2007; 275-277.
  13. Kulahci M, Almaz F. Some characterizations of osculating curves in the lightlike cone. Bol. Soc. Paran. Math. 2017; 35(2): 39-48, 2017.
  14. Kulahci MA, Almaz F, Bektaş M. On helices and slant helices in the lightlike cone. Honam Mathematical J. 2018; 40(2): 305-314.
  15. Liu H. Curves in the lightlike cone. Contributions to Algebra and Geometry Volume 2004; 45(1): 291-303.
  16. Millman RS, Parker GD. Elements of differential geometry, Prentice-Hall Inc. Englewood Cliffs, N. J., 1977.
  17. Onder M, Kocayigit H. Kazaz M. Spacelike helices in Minkowski 4-Space E14 Ann Univ. Ferrara 2010; 56: 335-343.
  18. O’Neill B. Semi-Riemannian Geometry, Academic Press, New York, 1983.
  19. Turgut M, Yilmaz S. Some Characterizations of type-3 slant helices in Minkowski Space-time. Involve 2009; 2(1): 115-121.