New Classications for Space-like Curves in the Null Cone

Abstract

In the Euclidean space E³ , the notion of rectifying curves is introduced by Chen [3] as a curve whose position vector always lying in its rectifying plane spanned by the tangent and binormal vector field of the curve. This study provides classifications of spacelike curves in the null cone. Spacelike rectifying curves lying fully in the 2-dimensional null cone and 3-dimensional null cone are characterized.Also,necessary and sufficient conditions are obtained for such curve to be a Tzitzeica curve in the 3-dimensional null cone. Furthermore, example is given for these curves.