On Nonlightlike Curves in Minkowski Space-time

In this paper, some special nonlightlike curves are investigated depending on characterizations of their Serret-Frenet frames in Minkowski space-time. Firstly, a great survey of nonlightlike curves in Minkowski space-time is stated. To generalize the results, the nonlightlike curves with the character of Serret-Frenet frame (ε₁,ε₂,ε₃,ε₄) are considered. So that, the necessary or/and sufficient conditions of a given nonlightlike curve to be a straight line, plane curve, helix and to lie on pseudohyperbolical space H₀³(r) and Lorentzian hypersphere S₀³(r) are stated both depending on curvature functions and character of Serret-Frenet frame of the curve, respectively.

Keywords:

Minkowski Space-time, Nonlightlike Curve Serret-Frenet Frame,

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[1] Gokc¸elik F., Bozkurt Z., Gok ˙I., Ekmekc¸i F.N., Yaylı Y., Parallel Transport Frame in 4- Dimensional Euclidean Space E4: Caspian Journal of Sciences, 3 (2014), pp:91-102.
[2] Magden A., Characterizations of Some Special curves in E4; Dissertation, Dept. Math. Atat¨urk University, Erzurum, TURKEY, 1990.
[3] Turgut M., Ali A.T., Some Characterizations of Special Curves in Euclidean Space E4; Acta Univ. Sapientiae, Mathematica, 2 (2010), pp:111-122.
[4] Walrave J., Curves and Surfaces in Minkowski Space, Doctoral Thesis, K.U. Leuven, Fac. of Science, Leuven (1995).
[5] Yılmaz S., Turgut M., On the Differential Geometry of the Curves in Minkowski Space-time I, Int. J. Contemp. Math. Science, 3(2008), pp:1343-1349.
[6] Camcı C, Ilarslan K., Sucurovic E., On Pseudohyperbolical Curves in Minkowski Space-time, Turkish Journal of Mathematics, 27 (2003), pp:315-328.
[7] Turgut M., Yılmaz S., Characterization of Some Spacelike Curves in Minkowski Space-time, International J. Math. Combin., 2(2008), pp:17-22.
[8] Erdogdu M., Parallel frame of non-lightlike curves in Minkowski space-time, International Journal of Geometric Methods in Modern Physics, 12 (2015), pp:1-16.
[9] Ozdemir M., Ergin A.A., Parallel Frames of Non-Lightlike Curves, Missouri Journal of Mathematical Sciences, 20 (2008), pp:127-137.
[10] Magden A., On the curves of constant slope, YYU Fen Bilimleri Dergisi, 4(1993), pp: 103-109.
[11] ¨Onder M., Kocayigit H., Kazaz M., Spacelike Helices in Minkowski 4-Space E41, Ann Univ Ferrara, 56 (2010), pp:335–343.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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