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Year 2021, Volume: 42 Issue: 4, 906 - 915, 29.12.2021

Fatma Bulut

Abstract

References

  • [1] Ali A.T., Turgut M., Some characterizations of slant helices in the Euclidean space E^n, Hacet. J. Math. Stat., 39 (3) (2010) 327–33.
  • [2] Abdel-Aziz H.S., Saad M.K., Abdel-Salam A.A., Equiform Differential Geometry of Curves in Minkowski Space-Time, https://arxiv.org/abs/1501.02283, (2015).
  • [3] İlarslan K., Nešović E., Spacelike and Timelike Normal Curves in Minkowski Space-Time, Publications de L’Institut Mathematique, Nouvelle série, tome, 85 (99) (2009) 111-118.
  • [4] Aydın M.E., Ergüt M., The equiform differential geometry of curves in 4-dimensional Galilean space G_4, Stud. Univ. Babes-Bolyai Math., 58 (3) (2013) 399–406.
  • [5] Turgut M., Yilmaz S., Characterizations of Some Special Spacelike Curves in Minkowski eg-time, International J.Math. Combin., (2) (2008) 17-22. [6] Yılmaz M.Y., Bektaş M., Slant helices of (k,m)-type in E^4, Acta Univ. Sapientiae, Mathematica, 10 (2) (2018) 395–401.
  • [7] Yilmaz S., Turgut M., On the characterizations of inclined curves in Minkowski space-time E_1^4, International Mathematical Forum, 3 (16) (2008) 783-792.
  • [8] Gluck H., Higher curvature of curves in Euclidean space, Amer. Math. Monthly, 73 (1996) 699–70.
  • [9] Miroslava P.T., Emilija S., W-curves in Minkowski space-time, Novi Sad J. Math., 32 (2) (2002) 55-65.
  • [10] Bektas M., Ergüt M., Soylu D., The Characterization of the Spherical Timelike Curves in 3- Dimensional Lorentzian Space, Bull. Malaysian Math. Soc. (Second Series), 21 (1998) 11-125.
  • [11] İlarslan K., Spacelike normal curves in Minkowski space E_1^3, Turk J Math., 29 (2005) 53-63.
  • [12] Bulut F., Bektaş M., Special Helices On Equiform Differential Geometry of Spacelike Curves in Minkowski Space-Time, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69 (2) (2020) 51-62.
  • [13] O’Neill B., Semi Riemannian geometry, Academic Press, New York-London (1983).

Special helices on equiform differential geometry of timelike curves in E_1^4

Year 2021, Volume: 42 Issue: 4, 906 - 915, 29.12.2021

Fatma Bulut

Abstract

In this paper, we introduce the moving Frenet frame along the timelike curve in E_1^4 and then Frenet formulas with the equiform parameter in the equiform geometry of the Minkowski space-time. We obtain k-type helices for equiform differential geometry of timelike curves in Minkowski space-time E_1^4, in terms of their curvature functions. We give some new characterizations for these helices and investigate the special helices in Minkowski space-time. Finally, we establish (k,m)-type slant helices for equiform differential geometry of timelike curves in E_1^4.

Keywords

Equiform Frenet Frame Curvatures Minkowski 4-space

References

  • [1] Ali A.T., Turgut M., Some characterizations of slant helices in the Euclidean space E^n, Hacet. J. Math. Stat., 39 (3) (2010) 327–33.
  • [2] Abdel-Aziz H.S., Saad M.K., Abdel-Salam A.A., Equiform Differential Geometry of Curves in Minkowski Space-Time, https://arxiv.org/abs/1501.02283, (2015).
  • [3] İlarslan K., Nešović E., Spacelike and Timelike Normal Curves in Minkowski Space-Time, Publications de L’Institut Mathematique, Nouvelle série, tome, 85 (99) (2009) 111-118.
  • [4] Aydın M.E., Ergüt M., The equiform differential geometry of curves in 4-dimensional Galilean space G_4, Stud. Univ. Babes-Bolyai Math., 58 (3) (2013) 399–406.
  • [5] Turgut M., Yilmaz S., Characterizations of Some Special Spacelike Curves in Minkowski eg-time, International J.Math. Combin., (2) (2008) 17-22. [6] Yılmaz M.Y., Bektaş M., Slant helices of (k,m)-type in E^4, Acta Univ. Sapientiae, Mathematica, 10 (2) (2018) 395–401.
  • [7] Yilmaz S., Turgut M., On the characterizations of inclined curves in Minkowski space-time E_1^4, International Mathematical Forum, 3 (16) (2008) 783-792.
  • [8] Gluck H., Higher curvature of curves in Euclidean space, Amer. Math. Monthly, 73 (1996) 699–70.
  • [9] Miroslava P.T., Emilija S., W-curves in Minkowski space-time, Novi Sad J. Math., 32 (2) (2002) 55-65.
  • [10] Bektas M., Ergüt M., Soylu D., The Characterization of the Spherical Timelike Curves in 3- Dimensional Lorentzian Space, Bull. Malaysian Math. Soc. (Second Series), 21 (1998) 11-125.
  • [11] İlarslan K., Spacelike normal curves in Minkowski space E_1^3, Turk J Math., 29 (2005) 53-63.
  • [12] Bulut F., Bektaş M., Special Helices On Equiform Differential Geometry of Spacelike Curves in Minkowski Space-Time, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69 (2) (2020) 51-62.
  • [13] O’Neill B., Semi Riemannian geometry, Academic Press, New York-London (1983).
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Fatma Bulut 0000-0002-7684-6796

Publication Date December 29, 2021
Submission Date July 5, 2021
Acceptance Date November 30, 2021
Published in Issue Year 2021Volume: 42 Issue: 4

Cite

APA Bulut, F. (2021). Special helices on equiform differential geometry of timelike curves in E_1^4. Cumhuriyet Science Journal, 42(4), 906-915.