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Dergiler / Fundamental Journal of Mathematics and Applications / 2022 / Cilt: 5 Sayı: 3

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Osman Zeki OKUYUCU
Bahar DOĞAN YAZICI
Sayfa
201–209
Yayın Tarihi
2022-09-23
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in $3D$ Euclidean space and in $3D$ Lie groups.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics.
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Temel Bulgular & Veri:In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics.
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Sonuç & Katkı:In this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in $3D$ Euclidean space and in $3D$ Lie groups.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Generalized Bertrand curves · Generalized Mannheim curves · Helix

Abstract

In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics. In this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in $3D$ Euclidean space and in $3D$ Lie groups.

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Bu Makaleye Atıf Yap

OKUYUCU, O. Z., YAZICI, B. D. (2022). Generalized Bertrand and Mannheim Curves in 3D Lie Groups. Fundamental Journal of Mathematics and Applications, Cilt: 5 Sayı: 3, 201–209. https://ajindex.com/articles/905664

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Kaynakça (19)

  1. M. A. Lancret, Memoire sur les courbes `a double courbure, M´emoires pr´esent´es `a l’Institut1, 1806, 416–454
  2. B. Altunkaya, L. Kula, General helices that lie on the sphere S2n in Euclidean space E2n+1, Uni. J. Math. App., 1(3) (2018), 166-170
  3. S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math., 28 (2004), 153-163
  4. J. M. Bertrand, Memoire sur la th´eorie des courbes ´a double courbure, Comptes Rendus, 36 (1850)
  5. H. Liu, F. Wang, Mannheim partner curves in 3-space, J. Geom., 88 (2008), 120–126
  6. M. Akyigğt, S. Ersoy, İ. Özgür, M. Tosun, Generalized timelike Mannheim curves in Minkowski space-time E4_1, Mathematical Problems in Engineering, Article ID 539378, (2011), 19 p
  7. S. Ersoy, M. Akyiğit, M. Tosun, A note on admissible Mannheim curves in Galilean space G3, Math. Combinatorics, 1 (2011), 88-93
  8. S. Ersoy, M. Masal, M. Tosun, On Mannheim partner curves of AW(k)-type, Uzbek Math. J., 1 (2014), 97-107
  9. M. S. Lone, H. Es, M. K. Karacan, B. B¨ukc¨u, Mannheim curves with modified orthogonal frame in Euclidean 3-space, Turk. J. Math., 43 (2) (2019), 648-663
  10. Ç. Camcı, A. Uc¸um, K. ˙Ilarslan, A new approach to Bertrand curves in Euclidean 3-space, J. Geom., 111 (49) (2020)
  11. A. Uçum, Ç. Camcı, K. ˙Ilarslan, A new approach to Mannheim curve in Euclidean 3-space, Tamkang J. Math., 54, (2021)
  12. Ü. Çiftçi, A generalization of Lancert’s theorem, J. Geom. Phys., 59 (2009), 1597-1603
  13. O. Z. Okuyucu, İ. Gök, Y. Yaylı, N. Ekmekc¸i, Slant helices in three dimensional Lie groups, Appl. Math. Comput., 221 (2013), 672–683
  14. İ Gök, O. Z. Okuyucu, N. Ekmekçi, Y. Yaylı, On Mannheim partner curves in three dimensional Lie groups, Miskolc Math. Notes, 15(2) (2014), 467–479
  15. O. Z. Okuyucu, İ. Gök, Y. Yaylı, N. Ekmekc¸i, Bertrand curves in three dimensional Lie groups, Miskolc Math. Notes, 17(2) (2017), 999–1010
  16. O. Z. Okuyucu, Ö. G. Yıldız, M. Tosun, Spinor Frenet equations in three dimensional Lie groups, Adv. Appl. Clifford Algebras, 26 (2016), 1341–1348
  17. O. Z. Okuyucu, C. Deg˘irmen, O¨. G. Yıldız, Smarandache curves in three dimensional Lie groups, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 1175-1185
  18. M. Mak, Natural and conjugate mates of Frenet curves in three-dimensional Lie group, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 70(1) (2021), 522-540
  19. G. Yıldız, O. Z. Okuyucu, Inextensible flows of curves in Lie groups, Caspian J. Math