EN
Special helices on equiform differential geometry of timelike curves in E_1^4
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
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Fatma Bulut
*
0000-0002-7684-6796
Türkiye
Publication Date
December 29, 2021
Submission Date
July 5, 2021
Acceptance Date
November 30, 2021
Published in Issue
Year 1970 Volume: 42 Number: 4