One-parameter homothetic motion in the Minkowski 3-space

Abstract

A one-parameter homothetic motion in three-dimensional Minkowski space is defined by means of the Hamilton operators. We study some properties of this motion and show that it has only one pole point at every instant t. We also obtain the Darboux vector of the homothetic motion in E³? and show that it can be written as multiplication of two split quaternions.