Split quaternions and the bisector surfaces obtained by two spatial curves in Minkowski 3-space

Abstract

In this paper, we investigate the bisector surfaces generated by spatial curves via split quaternions in E-1(3). We consider the bisector surfaces between two split quaternionic curves in Minkowski 3-space. This case is shown to yield rational bisector surfaces. Moreover, we give degenerate cases of these curves. Then, we provide some examples of rational bisector surfaces of two spatial quaternionic curves.