Different Approach by System of Differential Equations for the Characterization Position Vector of Spacelike Curves

Abstract

The purpose of this study is to obtain a characterization of unit speed spacelike curve with constant curvature and torsion in the Minkowski 3-space. According to this purpose, the position vector of a spacelike curve is expressed by a linear combination of its Serret Frenet Frame with differentiable functions. Since a spacelike curve has different kinds of frames, then we investigate the curve with respect to the Lorentzian casual characterizations of the frame. Hence we examine the results in three different cases including different subcases. Moreover, we illustrate some examples for each case.