Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31903
Position Vector of a Partially Null Curve Derived from a Vector Differential Equation

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu


In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1029


[1] W.B. Bonnor, "Null curves in a Minkowski space-time", Tensor. Vol. 20, pp. 229-242, 1969.
[2] C. Camci, K. Ilarslan and E. Sucurovic, "On pseudohyperbolical curves in Minkowski space-time". Turk J.Math. vol. 27, pp. 315-328, 2003.
[3] B.Y. Chen, "A report on submanifolds of finite type", Soochow J. Math. vol. 22 pp. 1-128, 1996.
[4] B.Y. Chen, F. Dillen and L. Verstraelen, "Finite type space curves", Soochow J. Math. vol. 12 pp. 1-10, 1986.
[5] B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
[6] M. Petrovic-Torgasev and E. Sucurovic, "W-Curves in Minkowski Space-time". Novi Sad J. Math. vol. 32, no. 2 pp. 55-65, 2002.
[7] M. Petrovic-Torgasev, K.Ilarslan and E. Nesovic, "On partially null and pseudo null curves in the semi-euclidean space 4 R2 ". J. of Geometry. vol. 84, pp. 106-116, 2005.
[8] J. Walrave, "Curves and surfaces in Minkowski space" Ph.D. dissertation, K. U. Leuven, Fac. of Science, Leuven 1995.
[9] S. Y─▒lmaz, "Determination of Space-like curves by Vector Differential Equations in Minkowski space 3 E1 ". J. Avd. Res.Pure Math. vol. 1 no. 1 pp. 10-14, 2009.