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Journals / Konuralp Journal of Mathematics / 2021 / Cilt: 9 Sayı: 2

Quaternionic $\left( 1,3\right) -$ Bertrand Curves According to Type 2-Quaternionic Frame in $\mathbb{R}^{4}$

Ferdağ KAHRAMAN AKSOYAK
Pages
346–355
Publication Date
2021-10-15
DOI
—
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AI Summary & Key Takeaways

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

Hence by using the method which is given by Matsuda and Yorozu [13], we give the denition of quaternionic $(1,3)-$Bertrand curve according to Type 2-Quaternionic Frame and obtain some results about these curves.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:If there exists a quaternionic Bertrand curve in $\mathbb{E}^{4}$, then its torsion or bitorsion vanishes.
📊
Key Findings & Data:So we can say that there is no quaternionic Bertrand curves whose torsion and bitorsion are non-zero.
💡
Conclusion & Impact:Hence by using the method which is given by Matsuda and Yorozu [13], we give the denition of quaternionic $(1,3)-$Bertrand curve according to Type 2-Quaternionic Frame and obtain some results about these curves.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quaternions · Quaternionic frame · Bertrand curve

Abstract

If there exists a quaternionic Bertrand curve in $\mathbb{E}^{4}$, then its torsion or bitorsion vanishes. So we can say that there is no quaternionic Bertrand curves whose torsion and bitorsion are non-zero. Hence by using the method which is given by Matsuda and Yorozu [13], we give the denition of quaternionic $(1,3)-$Bertrand curve according to Type 2-Quaternionic Frame and obtain some results about these curves.

🔖

Cite This Article

AKSOYAK, F. K. (2021). Quaternionic $\left( 1,3\right) -$ Bertrand Curves According to Type 2-Quaternionic Frame in $\mathbb{R}^{4}$. Konuralp Journal of Mathematics, Cilt: 9 Sayı: 2, 346–355. https://ajindex.com/articles/908867

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References (17)

  1. Bertrand J. M., Memoire sur la theorie des courbes a double courbure, Comptes Rendus, 15, 332-350, 1850
  2. Bharathi K., Nagaraj M., Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math. 18 (6) 507-511
  3. Çetin M. Kocayiğit H., On the quaternionic Smarandache curves in Euclidean 3-space, Int.J. Contemp Math Sci 8(3), 139-150, 2013
  4. Ersoy S., Tosun M., Timelike Bertrand curves in semi-Euclidean space, Int. J. Math. Stat., 14(2), 78-89, 2013
  5. Gök İ., Okuyucu O.Z., Kahraman F., Hacısalihoğlu H. H., On the quaternionic B2-slant helices in the Euclidean space E4: Adv. Appl. Cli ord Algebr., 21, 707-719, 2011
  6. Gök İ., Kaya Nurkan S., İlarslan K., On pseudo null Bertrand curves in Minkowski space-time, Kyungpook Math. J. 54(4), 685-697, 2014
  7. Güngör M. A. and Tosun M., Some characterizations of quaternionic rectifying curves, Di er. Geom. Dyn. Syst. 13, 89-100, 2011
  8. Irmak Y., Bertrand Curves and Geometric Applications in Four Dimensional Euclidean Space, MSc thesis, Ankara University, Institute of Science, 2018
  9. Kahraman Aksoyak F., Gök İ., İlarslan K., Generalized null Bertrand curves in Minkowski space-time, An. Ştiint. Univ. Al. I. Cuza, Iasi, Mat. (N.S.) 60 (2), 489-502, 2014
  10. Kahraman Aksoyak F., A new type of quaternionic Frame in R4; Int. J. Geom. Methods Mod. Phys., 16 (6), 1950084 (11 pages), 2019
  11. Karadağ M., Sivridağ A., Quaternion valued functions of a single real variable and inclined curves, Erciyes Univ. J. Inst. Sci. Technol 13, 23-36,1997
  12. Keçilioğlu O., İlarslan K., Quaternionic Bertrand curves in Euclidean 4- space. Bull. Math. Anal. Appl. 5 (3), 27{38, 2013
  13. Matsuda H. and Yorozu S., Notes on Bertrand curves. Yokohama Math. J. 50 (1-2), 41-58, 2003. [14]  Önder M., Quaternionic Salkowski curves and quaternionic similar curves, Proc. Natl. Acad. Sci. India, Sect. A Phys. Sci., 90 (3), 447-456, 2020. [15]  Öztürk G., Kişi İ., Büyükkütük S., Constant ratio quaternionic curves in Euclidean spaces. Adv. Appl. Cli ord Algebr. 27 (2), 1659-1673, 2017
  14. Pears L. R., Bertrand curves in Riemannian space, J. London Math. Soc. 1-10 (2), 180-183, 1935
  15. Şenyurt S., Cevahir C., Altun Y., On spatial quaternionic involute curve a new view. Adv. Appl. Cli ord Algebr. 27 (2), 1815-1824, 2017
  16. Uçum A., İlarslan K., Sasaki M., On (1,3)-Cartan null Bertrand curves in semi-Euclidean 4-space with index 2, J. Geom., 107 (3), 579-591, 2016
  17. Uçum A., Keçilio