New results concerning Cartan null and pseudo null curves in Minkowski 3-space

Abstract

In this study, we focus on Cartan null and pseudo null curves in Minkowski 3-space E13 . Firstly we define Cartan null and pseudo null equivalent curves and give the related examples. Then we give a construction method for Cartan null curves and it is shown that every Cartan null curve can be obtained from a timelike curve lying in the Lorentz plane in E13 . Also a construction method is given for pseudo null curves and we show that all pseudo null curves lie in a lightlike plane in E13 . Finally we define a new surface in E13 called “surface of pseudo null curves” and we obtain the geometric properties of such surfaces.