Geometrical Analysis of Spacelike and Timelike Rectifying Curves and their Applications

Abstract

In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and their uses in various fields, we are interested here to study a special kind of curves called rectifying curves. We consider some characterizations of a non-lightlike curve has a spacelike or timelike rectifying plane in pseudo-Euclidean space E13. Then, we demonstrate that the proportion of curvatures of any spacelike or timelike rectifying curve is a non-constant linear function of the arc length parameter s. Finally, we defray a computational example to support our main findings.