Buddhadev PAL, Akhılesh YADAV

18713

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

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

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 $\mathbb{H}^3(-r)$.
Keywords:

rectifying curve, general helix geodesic, hyperbolic space $\mathbb{H}^3(-r)$,

PDF

___

  • [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.
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: Yılda 6 Sayı
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
Arşiv
Sayıdaki Diğer Makaleler

Zahid Iqbal, Muhammad Ishaq, Muhammad Ahsan Binyamin

Ling Zhu, Branko Malešević

Rashid Mehmood, Muhammad Hisyam Lee, Iftikhar Ali, Muhammad Riaz

Chillumuntala Jayaram, Ünsal Tekir, Suat Koç

Dirk Veestraeten

Jia Bao Liu, Shaohui Wang, Chunxiang Wang

Morteza Noferesti, Hosein Fazaeli Moghimi, Mohammad Hossein Hosseini

Morteza Fatehi, Kazem Khashyarmanesh, Abbas Mohammadian

Onur Toka, Meral Çetin, Olcay Arslan

Şenay Asma