THE CHARACTERIZATIONS OF SPACELIKE CURVES IN R4

Abstract

In this paper, we study the geometry of position vectors of a spacelike curve in the Minkowski 4-space. We give some characterizations for spacelike curves to lie on some subspaces of R4 1.

Keywords

• Spacelike curve,Frenet frame,Minkowski spacetime

References

1. [1] A.C. Coken, and U. Ciftci, On the Cartan Curvatures of a Null Curve in Minkowski Space- time, Geometriae Dedicate 114 (2005), 71-78.
2. [2] A. Fernandez, A. Gimenez, and P. Lucas, Null helices in Lorentzian space forms, Int. J. Mod. Phys. A. 16 (2001), 4845-4863.
3. [3] A. T. Ali, M. Onder, Some Characterizations of Rectifying Spacelike Curves in the Minkowski Space-Time, Global J of Sciences Frontier Research Math, Vol 12, Is 1, 2012 2249-4626
4. [4] C. Camci, K. Ilarslan, L. Kula, H.H. Hacisalihoglu, Harmonic Curvatures and Generalized Helices in En, Chaos,Solitions and Fractals 40 (2009), 2590-2596.
5. [5] K. Ilarslan, and O. Boyacioglu, Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos,Solitions and Fractals (2008), 1383-1389.
6. [6] K. Ilarslan, Spacelike Normal Curves in Minkowski E3 1 , Turk. J. Math 29(2005), 53-63
7. [7] K. Ilarslan, E. Nesovic, M. Petrovic-Torgasev, Some Characterizations of Rectifying Curves in Minkowski 3-space, Novi Sad J Math 2003, 33(2), 23-32
8. [8] K. Ilarslan, E. Nesovic, Spacelike and timelike normal curves, , Publications de l'Institut Mathmatique (Beograd) Nouvelle serie, tome 85(99) (2009) 111-118.

9. [9] K. Ilarslan, E. Nesovic, Some characterizations of rectifying curves in the Euclidean space E4., Turkish J. Math. 32 (2008), no. 1, 21-30
10. [10] K. Ilarslan, and E. Nesovic, Some characterizations of null osculating curves in the Minkowski space-time, Proceedings of the Estonian Academy of Sciences, 61, I (2012), 1-8.
11. [11] M. Onder, H. Kocayigit and M. Kazaz, Spacelike Helices in Minkowski 4-space, Ann. Univ. Ferrera 2010, 56, 335-343
12. [12] S. KELES, S. Y. PERKTAS and E. KILIC, Biharmonic Curves in LP-Sasakian Manifolds, Bulletin of the Malasyian Mathematical Society, (2) 33(2), 2010, 325-344
13. [13] M. A. Akgun, A. I. Sivridag, On The Null Cartan Curves of R4 1, Global Journal of Mathe- matics, Vol.1 No.1,2015,41-50
14. [14] M. A. Akgun, A. I. Sivridag, On The Characterizations of Timelike Curves in R4 1, Global Journal of Mathematics, Vol.2 No.2,2015,116-127
15. [15] M. A. Akgun, A. I. Sivridag, Some Characterizations of a Spacelike Curve in R4 1, Pure Mathematical Sciences, Hikari Ltd., Vol.4 No.1-4,2015,43-55