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Journals / Hagia Sophia Journal of Geometry / 2022 / Cilt: 4 Sayı: 2

New Associated Curves $k-$Principle Direction Curves and $N_{k}-$Slant Helix

Çağla Ramis(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0000-0002-2809-8324
Beyhan Yılmaz(KAHRAMANMARAS SUTCU IMAM UNIVERSITY)0000-0002-5091-3487
Yusuf Yaylı(ANKARA UNIVERSITY)0000-0003-4398-3855
Pages
19–27
Publication Date
2022-12-30
DOI
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AI Summary & Key Takeaways

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

The new curve characterization called as $N_{k}-$slant helix, which is an improved version of existing helices, is obtained as a fundamental outcome.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present an alternative orthonormal frame system for spatial curves defined by principal directions in $3−$dimensional Euclidean space.
📊
Key Findings & Data:In this study, we present an alternative orthonormal frame system for spatial curves defined by principal directions in $3−$dimensional Euclidean space.
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Conclusion & Impact:The new curve characterization called as $N_{k}-$slant helix, which is an improved version of existing helices, is obtained as a fundamental outcome.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Slant helix · Clad helix · direction curve

Abstract

In this study, we present an alternative orthonormal frame system for spatial curves defined by principal directions in $3−$dimensional Euclidean space. The new curve characterization called as $N_{k}-$slant helix, which is an improved version of existing helices, is obtained as a fundamental outcome.

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Cite This Article

Ramis, Ç., Yılmaz, B., Yaylı, Y. (2022). New Associated Curves $k-$Principle Direction Curves and $N_{k}-$Slant Helix. Hagia Sophia Journal of Geometry, Cilt: 4 Sayı: 2, 19–27. https://ajindex.com/articles/1490443

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References (17)

  1. Frenet, F. (1852). Sur les courbes a double courbure. Journal de Mathematiques Pures et Appliquees, 17, 437-447.
  2. Serret, J. A. (1851). Sur quelques formules relatives a la theorie des courbes a double courbure. Journal de Mathematiques Pures et Appliquees, 16, 193-207.
  3. Kühnel, W. (2005). Differential geometry: curves - surfaces - manifolds. Vol. 16, American Mathematical Society.
  4. Struik, D. J. (1988). Lectures on classical differential geometry, Dover, New-York.
  5. Lancret, M. A. (1806). Memoire sur les courbesa double courbure. Memoires Presentes AlInstitut, 1, 416-454.
  6. Izumiya, S., & Takeuchi, N. (2004). New special curves and developable surfaces. Turkish Journal of Mathematics, 28(2), 153-164.
  7. Scofield, P. D. (1995). Curves of constant precession. The American mathematical monthly, 102(6), 531-537.
  8. Takahashi, T., & Takeuchi, N. (2014). Clad helices and developable surfaces. Bulletin of Tokyo Gakugei University Division of Natural Sciences, 66, 1-9.
  9. Hanson, A. J., & Ma H. (1995). Parallel transport approach to curve framing. Indiana University, Techreports-TR425, 11, 3-7.
  10. Wang, W., Juttler, B., Zheng, D., & Liu, Y. (2008). Computation of rotation minimizing frames. ACM Transactions on Graphics (TOG), 27(1), 1-18.
  11. Bishop, R. L. (1975). There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251.
  12. Uzunoğlu, B., Gök, ̇I., & Yaylı, Y. (2016). A new approach on curves of constant precession. Applied Mathematics and Computation, 275, 317-323.
  13. Uzunoğlu, B., Ramis, C ̧., & Yaylı, Y. (2014). On curves of $N_{k}-$slant helix and $N_{k}-$constant precession in Minkowski 3-space. Journal of Dynamical Systems and Geometric Theories, 12(2), 175-189.
  14. O’Neill, B. (1966). Elementary differential geometry. Academic Press, New York.
  15. Choi, J. H., & Kim, Y. H. (2012). Associated curves of a Frenet curve and their applications. Applied Mathematics and Computation, 218(18), 9116-9124.
  16. Ali, T. A. (2009). New special curves and their spherical indicatrices. arXiv preprint arXiv:0909.2390v1 [math.DG].
  17. Uzunoğlu, B., Ramis, C ̧., & Yaylı, Y. (2014). On curves of $N_{k}-$slant helix and $N_{k}-$constant precession in Minkowski 3-space. Journal of Dynamical Systems and Geometric Theories, 12(2), 175-189.