A Study on a Partially Null Curve in E₂⁴

Abstract

In this paper, we study with Frenet equations which are given in [3] of a partially null curve in Semi- Euclidean 4-space E₂⁴ with index 2. By using the Frenet equations, we give some theorem and corollary. A characterization of a  hyperbolic partially null curve in E₂⁴ is given. Additionally, we examine harmonic curvatures and curvatures of this curve in E₂⁴

Keywords

• Partially null curve,Semi-Euclidean space E₂⁴,Frenet frame,curvatures

References

1. O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
2. Turgut, M. and Yılmaz S., Some characterizations of partially null curves in Semi-Euclidean Space, International Mathematical Forum, (2008), 32(3), 1569-1574.
3. Petrovic-Torgasev M., İlarslan, K. and Nesovic E., On partially null and pseudo null curves in the Semi-Euclidean space R₂^{4 }, J. Geom., (2005), 84, 106-116.
4. Yılmaz, S. and Turgut M., On Frenet apparatus of partially null curves in Semi-Euclidean space, Scientia Magna, (2008), 4(2), 39-44.
5. Petrovic-Torgasev, M. and Sucurovic E., Some characterizations of the spacelike, the timelike and the null curves on the pseudohyperbolic space H₀² in E₁³, Kragujevac J. Math., (2000), 22, 71-82.
6. İyigün, E. and Arslan K., On harmonic curvatures of curves in Lorentzian n-space, Commun. Fac. Sci.Univ. Ank. Series A1., (2005), 54(1), 29-34.