Spacelike normal curves in Minkowski space $Bbb{E}_1^3$

In the Euclidean space $Bbb{E}^3$, it is well known that normal curves, i.e., curves with position vector always lying in their normal plane, are spherical curves [3]. Necessary and sufficient conditions for a curve to be a spherical curve in Euclidean 3-space are given in [10] and [11]. In this paper, we give some characterizations of spacelike normals curves with spacelike, timelike or null principal normal in the Minkowski 3-space $Bbb{E}_1^3$.

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[1] Bonnor, W. B.: Null Curves in a Minkowski space-time, Tensor, 20, 1969, 229-242.
[2] Camcı, Ç., İlarslan, K. and Sucurovic, E.: On pseudohyperbolic curves in Minkowski spacetime, Turkish Journal of Math., 27, 315-328, 2003.
[3] Chen, B. Y.: When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Mounthly, 110, 2003, 147-152.
[4] Ekmekci N. and İlarslan, K.: Higher Curvatures of a Regular Curve in Lorentzian Space,Journal of Institute of Math. and Comp. Sci., Vol. 11, No. 2, 1998, 97-102.
[5] İlarslan, K., Nesovic, E. and Petrovic-Torgasev, M.: Some Characterizations of Rectifying Curves in the Minkowski 3-space, Novi Sad J. Math. Vol 33, No. 2, 2003, 23-32.
[6] O`Neill, B.: Semi - Riemannian geometry, with applications to relativity. Academic Press. New York, 1983.
[7] Petrovic-Torgasev, M. and Sucurovic,E.: Some characterizations of Lorentzian spherical spacelike curves with the timelike and null principal normal, Mathematica Moravica, 4,2000, 83-92.
[8] Petrovic-Torgasev, M. and Sucurovic, E.: Some characterizations of curves lying on the pseudohyperbolic space $Bbb{H}^2_0$ in the Minkowski space $Bbb{E}^3_1$ , Kragujevac J. Math., 22, 2000, 71-82.
[9] Walrave, J.: Curves and Surfaces in Minkowski Space, Ph.D. thesis, K. U. Leuven, Fac. of Science, Leuven, 1995.
[10] Wong, Y. C.: A global formulation of the condition for a curve to lie in a sphere, Monatschefte fur Mathematik, 67, 1963, 363-365.
[11] Wong, Y. C.: On a explicit characterization of spherical curves, Proceedings of the American Math. Soc., 34, 1972, 239-242.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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