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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 1

Some characterizations of rectifying curves in the 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$

Buddhadev Pal(Banaras Hindu University)0000-0002-1407-1016
Akhılesh Yadav(Banaras Hindu University)0000-0003-3990-857X
Pages
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Publication Date
2021-02-04
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AI Summary & Key Takeaways

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

Then we find the distance function and also give the general equations of the curvature and torsion of rectifying general helices in $\mathbb{H}^3(-r)$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the geometry of rectifying curves in the 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$.
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Key Findings & Data:Further we obtain the distance function in terms of arc length when the rectifying curve lying in the upper half plane.
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Conclusion & Impact:Then we find the distance function and also give the general equations of the curvature and torsion of rectifying general helices in $\mathbb{H}^3(-r)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:rectifying curve · general helix · geodesic

Abstract

In this paper, we study the geometry of rectifying curves in the 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$. Further we obtain the distance function in terms of arc length when the rectifying curve lying in the upper half plane. Then we find the distance function and also give the general equations of the curvature and torsion of rectifying general helices in $\mathbb{H}^3(-r)$.

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Cite This Article

Pal, B., Yadav, A. (2021). Some characterizations of rectifying curves in the 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.554500

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References (8)

  1. P. Alegre, K. Arslan, A. Carriazo, C. Murathan and G. Ozturk, Some special types of developable ruled surface, Hacet. J. Math. Stat. 39 (3), 319–325, 2010.
  2. B. Altunkaya and L. Kula, On spacelike rectifying slant helices in Minkowski 3-space, Turkish J. Math. 42, 1098–1110, 2018.
  3. M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (5), 1503–1509, 1997.
  4. B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110, 147–152, 2003.
  5. S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turkish J. Math. 28 (2), 153–163, 2004.
  6. K. Ilarslan, E. Nesovic and M.P. Torgasev, Some characterization of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33 (2), 23–32, 2003.
  7. P. Lucas and J.A.O. Yagues, Rectifying curves in the three dimensional hyperbolic space, Mediterr. J. Math. 13, 2199–2214, 2016.
  8. P. Lucas and J.A.O. Yagues, Slant helices in the three dimensional sphere, J. Korean Math. Soc. 54 (4), 1331–1343, 2017.