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Dergiler / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 1 Issue: 1

Characterizations of slant and spherical helices due to pseudo-Sabban frame

Bülent Altunkaya
Levent Kula
Sayfa
—
Yayın Tarihi
2018-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.

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Amaç & Hipotez:In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.
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Temel Bulgular & Veri:In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.
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Sonuç & Katkı:In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Geodesic curvature · Sabban frame · Minkowski space

Abstract

In this paper, we investigate that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H^2,$ the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski 3-space.

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Bu Makaleye Atıf Yap

Altunkaya, B., Kula, L. (2018). Characterizations of slant and spherical helices due to pseudo-Sabban frame. Fundamental Journal of Mathematics and Applications, Volume: 1 Issue: 1. https://doi.org/10.33401/fujma.412081

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Kaynakça (15)

  1. Ali Ahmad, T. and Lopez, R., Slant helices in Minkowski space E3 1, J. Korean Math. Soc. 48, no. 1, 159–167. 2011.
  2. Altunkaya, B. and Kula, L., Some characterizations of slant and spherical helices due to sabban frame, Mathematical Sciences and Applications E-Notes, Vol 3, No. 2, 64-73, 2015.
  3. Babaarslan, M. and Yaylı, Y., On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space, Annals of the Alexandru Ioan Cuza University -Mathematics, 2015. doi:10.1515/aicu-2015-0009.
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  7. Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  8. Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space, arXiv:0810.3351v1 [math.DG], 2008.
  9. Pekmen, U¨. and Pas¸alı, S., Some characterizations of Lorentzian spherical spacelike curves, Mathematica Moravica 3, 31-37, 1999.
  10. Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical spacelike curves with the timelike and the null principal normal, Math. Moravica, 4, 83-92, 2000.
  11. Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of Lorentzian spherical timelike and null curves, Matematicki Vesnik, 53, 21-27, 2001.
  12. Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of the spacelike, the timelike and the on the pseudohyperbolic space H2 0 in E3 1, Krugajevac J. Math., 22, 71-82, 2000.
  13. Ali Ahmad, T. and Lopez, R., Slant helices in Minkowski space E3 1, J. Korean Math. Soc. 48, no. 1, 159–167. 2011.
  14. Pekmen, U¨. and Pas¸alı, S., Some characterizations of Lorentzian spherical spacelike curves, Mathematica Moravica 3, 31-37, 1999.
  15. Petrovic-Torgasev, M. and Sucurovic, E., Some characterizations of the spacelike, the timelike and the on the pseudohyperbolic space H2 0 in E3 1, Krugajevac J. Math., 22, 71-82, 2000.