### On the Characterizations of Spacelike Curves in R_1^4

#### Abstract

In this paper, we study the position vectors of a spacelike curve in the Minkowski 4-space*.* We give some characterizations for spacelike curves to lie on some subspaces and give some theorems for these curves. We give spacelike curves in terms of their curvature functions. By using these equations we give the position vectors of spacelike curves in terms of their curvature functions and in 4-dimensional Minkowski space.

**Keywords: **Spacelike curve, Frenet Frame, Minkowski Spacetime, Subspace, Curvature functions.

#### Full Text:

PDF#### References

A.C. Coken, and U. Ciftci, On the Cartan Curvatures of a Null Curve in Minkowski Spacetime, Geometriae Dedicate 114 (2005), 71-78.

A. Fernandez, A. Gimenez, and P. Lucas, Null helices in Lorentzian space forms, Int. J. Mod. Phys. A. 16 (2001), 4845-4863.

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

B. O’Neill, Semi Riemannian Geometry, Academic Press (1983).

C. Camci, K. Ilarslan, L. Kula, H.H. Hacisalihoglu, Harmonic Curvatures and Generalized Helices in En, Chaos,Solitions and Fractals 40 (2009), 2590-2596.

K. Ilarslan, Spacelike Normal Curves in Minkowski E_1^3, Turk. J. Math., 29(2005), 53-63

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.

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.

K. Ilarslan, and E. Nesovic, Some characterizations of rectifying curves in the Euclidian space E^4, Turkish J. Math. 32(2008), no.1, 21-30

K. Ilarslan, E. Nesovic and M. Petrovic-Torgasev, Some Characterizations of Rectifying Curves in Minkowski 3-space, Novi Sad J Math 2003, 33(2), 53-63

M. Onder, H. Kocayigit and M. Kazaz, Spacelike helices in Minkowski 4-space, Ann. Univ. Ferrera 2010, 56, 335-343

S. Keles, S. Y. Perktas and E.Kilic, Biharmonic Curves in LP-Sasakian Manifolds, Bulletin of Malasyian Mathematical sciences Society,(2) 33(2),2010, 325-344

M. A. Akgun, A. I. Sivridag, On The Null Cartan Curves of R_1^4, Global Journal of Mathematics, Vol.1 No.1,2015,41-50

M. A. Akgun, A. I. Sivridag, On The Characterizations of Timelike Curves in R_1^4, Global Journal of Mathematics, Vol.2 No.2,2015,116-127

M. A. Akgun, A. I. Sivridag, Some Characterizations of a Spacelike Curve in R_1^4, Pure Mathematical Sciences, Hikari Ltd., Vol.4 No.1,2015,43-55.

### Refbacks

- There are currently no refbacks.

International Journal of Applied Physics & Mathematics is licensed under a Creative Commons Attribution 4.0 International License Based on a work at www.ijpm.ielas.org