Dual Cartan numbers and pseudo‐null lines

Abstract

The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number with lightlike dual vector also corresponds to a parabolic rotation and a translation transformation in the Cartan frame. Also, the angle between the directed pseudo‐null lines that tangent the same parabola is defined. Thus, the rotation and translation relationship between two directed pseudo‐null lines is obtained. Also, the E. Study transformation is given for the directed pseudo‐null lines.