Split quaternions and time-like constant slope surfaces in Minkowski 3-space

TL;DR

This paper demonstrates how time-like constant slope surfaces in Minkowski 3-space can be parametrized using split quaternions and homothetic motions, with illustrative examples provided.

Contribution

It introduces a novel parametrization method for time-like constant slope surfaces using unit time-like split quaternions and homothetic motions.

Findings

Time-like constant slope surfaces can be reparametrized with split quaternions.

Mathematica examples illustrate the reparametrization method.

The approach links quaternion algebra with geometric surface properties.

Abstract

In this paper, we prove that time-like constant slope surfaces can be reparametrized by using rotation matrices corresponding to unit time-like split quaternions and homothetic motions. Afterwards we give some examples to illustrate our main results by using Mathematica.