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Year 2020, , 327 - 343, 25.06.2020

Mahmut Mak

https://doi.org/10.17776/csj.686692

Abstract

References

  • [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] 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] 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] 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] Deshmukh S, Chen BY, Alshammari SH. On rectifying curves in Euclidean 3-space, Turkish Journal of Mathematics, 42(2) (2018) 609-620.
  • [6] İlarslan K, Nevsovic E., Some characterizations of rectifying curves in the Euclidean space, Turkish Journal of Mathematics, 32(1) (2008) 21-30.
  • [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] Izumiya S, Takeuchi N., New special curves and developable surfaces, Turkish Journal of Mathematics, 28(2) (2004) 153-163.
  • [9] Lucas P., Ortega J.Y., Rectifying curves in the three-dimensional sphere, Journal of Mathematical Analysis and Applications, 421(2) (2015) 1855-1868.
  • [10] Lucas P, Ortega JY. Rectifying curves in the three-dimensional hyperbolic space, Mediterranean Journal of Mathematics,13(4) (2016) 2199-2214.
  • [11] Chen L, Takahashi M. Dualities and evolutes of fronts in hyperbolic and de Sitter space, Journal of Mathematical Analysis and Applications, 37(1) (2016) 133-159.
  • [12] Huang J., Chen L., Izumiya S., Pei D., Geometry of special curves and surfaces in 3-space form, Journal of Geometry and Physics, 136 (2019) 31-38.
  • [13] Lucas P., Ortega J.Y., Bertrand curves in non-flat 3-dimensional (Riemannian or Lorentzian) space forms, Bulletin of the Korean Mathematical Society, 50(4) (2013) 1109-1126.
  • [14] O'Neill B., Semi-Riemannian Geometry with Applications to Relativity, London, UK: Academic Press Inc, 1983.

Some characterizations of timelike rectifying curves in de sitter 3 space

Year 2020, , 327 - 343, 25.06.2020

Mahmut Mak

https://doi.org/10.17776/csj.686692

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

Rectifying curve Conical surface Geodesic

References

  • [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] 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] 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] 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] Deshmukh S, Chen BY, Alshammari SH. On rectifying curves in Euclidean 3-space, Turkish Journal of Mathematics, 42(2) (2018) 609-620.
  • [6] İlarslan K, Nevsovic E., Some characterizations of rectifying curves in the Euclidean space, Turkish Journal of Mathematics, 32(1) (2008) 21-30.
  • [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] Izumiya S, Takeuchi N., New special curves and developable surfaces, Turkish Journal of Mathematics, 28(2) (2004) 153-163.
  • [9] Lucas P., Ortega J.Y., Rectifying curves in the three-dimensional sphere, Journal of Mathematical Analysis and Applications, 421(2) (2015) 1855-1868.
  • [10] Lucas P, Ortega JY. Rectifying curves in the three-dimensional hyperbolic space, Mediterranean Journal of Mathematics,13(4) (2016) 2199-2214.
  • [11] Chen L, Takahashi M. Dualities and evolutes of fronts in hyperbolic and de Sitter space, Journal of Mathematical Analysis and Applications, 37(1) (2016) 133-159.
  • [12] Huang J., Chen L., Izumiya S., Pei D., Geometry of special curves and surfaces in 3-space form, Journal of Geometry and Physics, 136 (2019) 31-38.
  • [13] Lucas P., Ortega J.Y., Bertrand curves in non-flat 3-dimensional (Riemannian or Lorentzian) space forms, Bulletin of the Korean Mathematical Society, 50(4) (2013) 1109-1126.
  • [14] O'Neill B., Semi-Riemannian Geometry with Applications to Relativity, London, UK: Academic Press Inc, 1983.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Mahmut Mak 0000-0003-3558-9161

Publication Date June 25, 2020
Submission Date February 8, 2020
Acceptance Date May 26, 2020
Published in Issue Year 2020

Cite

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