Research Article

Some characterizations of timelike rectifying curves in de sitter 3 space

Volume: 41 Number: 2 June 25, 2020
EN

Some characterizations of timelike rectifying curves in de sitter 3 space

Abstract

De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.

Keywords

References

  1. [1] Chen B.Y., When does the position vector of a space curve always lie in its rectifying plane? American Mathematical Monthly, 110(2) (2003) 147-152.
  2. [2] Kim D.S., Chung H.S., Cho K.H., Space curves satisfying τ/κ=as+b, Honam Mathematical Journal, 15(1) (1993) 5-9.
  3. [3] Chen B.Y., Dillen F., Rectifying curves as centrodes and extremal curves, Bulletin of the Institute of Mathematics Academia Sinica, 33(2) (2005) 77-90.
  4. [4] Chen B.Y., Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang Journal of Mathematics, 48(2) (2017) 209-214.
  5. [5] Deshmukh S, Chen BY, Alshammari SH. On rectifying curves in Euclidean 3-space, Turkish Journal of Mathematics, 42(2) (2018) 609-620.
  6. [6] İlarslan K, Nevsovic E., Some characterizations of rectifying curves in the Euclidean space, Turkish Journal of Mathematics, 32(1) (2008) 21-30.
  7. [7] Ilarslan K., Nevsovic E., Petrovic M.T., Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad Journal of Mathematics, 33(2) (2003) 23-32.
  8. [8] Izumiya S, Takeuchi N., New special curves and developable surfaces, Turkish Journal of Mathematics, 28(2) (2004) 153-163.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 25, 2020

Submission Date

February 8, 2020

Acceptance Date

May 26, 2020

Published in Issue

Year 2020 Volume: 41 Number: 2

APA
Mak, M. (2020). Some characterizations of timelike rectifying curves in de sitter 3 space. Cumhuriyet Science Journal, 41(2), 327-343. https://doi.org/10.17776/csj.686692

Cited By

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December