DUAL TIMELIKE NORMAL AND DUAL TIMELIKE SPHERICAL CURVES IN DUAL MINKOWSKI SPACE 3 D1

Abstract

In this paper, we give characterizations of dual timelike normal and dual timelike spherical curves in the dual Minkowski 3-space 3 D1 and we show that every dual timelike normal curve is also a dual timelike spherical curve.

Keywords

• Normal curves,Dual Minkowski 3-Space,Dual Timelike curves

D1 DUAL MINKOWSKI UZAYINDA DUAL TIMELIKE NORMAL VE DUAL TIMELIKE KÜRESEL EĞRİLER

Abstract

Bu çalışmada, 3 D1 dual Minkowski 3-uzayında dual timelike normal ve dual timelike küresel eğrilerin karakterizasyonları verildi ve her dual timelike normal eğrinin aynı zamanda bir dual timelike küresel eğri olduğu gösterildi.

Keywords

• Normal eğriler,Dual Minkowski 3-uzayı,Dual timelike eğriler

References

1. CAMCI, Ç., İLARSLAN, K. AND ŠUĆUROVIĆ, E., 2003: On pseudohyperbolic curves in Minkowski space-time, Turkish Journal of Math., 27, 315-328.
2. CHEN, B. Y., 2003. When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Mountly, 110, 147-152.
3. EKMEKÇI, N. AND İLARSLAN, K., 1998. Higher Curvatures of a Regular Curve in Lorentzian Space, Journal of Institute of Math. And Comp. Sci., Vol. 11, No 2, 97- 102.
4. İLARSLAN, K. 2005. Spacelike Normal Curves in Minkowski Space E , Turk Journal 3 1 of Math., 29, 53-63.
5. İLARSLAN, K., NEŠOVIĆ, E. AND PETROVIĆ-TURGAŠEV, M., 2003. Some Characterizations of Rectifying Curves in the Minkowski 3-space, Novi Sad J. Math. Vol. 33, No. 2, 23-32.
6. PETROVIĆ-TURGAŠEV, M. AND ŠUĆUROVIĆ, E., 2000. Some characterizations of Lorentzian spherical spacelike curves with the timelike and null principal normal, Mathematica Moravica, 4, 83-92.
7. PETROVIĆ-TURGAŠEV, M. AND ŠUĆUROVIĆ, E., 2000. Some characterizations of curves lying on the pseudohyperbolic space H in the Minkowski space E , 2 3 1 Kragujevac J. Math., 22, 71-82.
8. WONG Y. C., 1963. A global formulation of condition for a curve to lie in a sphere, Monatschefte fur Mathematik, 67, 363-365.

9. WONG Y. C., 1972. On an explicit characterization of spherical curves, Proceedings of the American Math. Soc., 34, 239-242.
10. YÜCESAN A., CÖKEN A. C., AYYILDIZ N., 2002. On the Dual Darboux Rotation Axis of the Timelike Dual Space Curve, Balkan Journal of Geometry and Its Applications, Vol. 7, No:2, 137-142.