Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space

Authors: Melih Turgut, Süha Yılmaz

Abstract:

In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328900

References:

[1] C. Boyer, A History of Mathematics, New York: Wiley,1968.
[2] W.B. Bonnor, "Null curves in a Minkowski space-time", Tensor. Vol. 20, pp. 229-242, 1969.
[3] C. Camci, K. Ilarslan and E. Sucurovic, "On pseudohyperbolical curves in Minkowski space-time". Turk J.Math. vol. 27, pp. 315-328, 2003.
[4] B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
[5] M. Petrovic-Torgasev, K.Ilarslan and E. Nesovic, "On partially null and pseudo null curves in the semi-euclidean space R24 ". J. of Geometry. Vol. 84, pp. 106-116, 2005.
[6] J. Walrave, "Curves and surfaces in Minkowski space" Ph.D. dissertation, K. U. Leuven, Fac. of Science, Leuven 1995.