Space-like Loxodromes on the Canal Surfaces in Minkowski 3-Space

TL;DR

This paper derives differential equations for space-like loxodromes on non-degenerate canal surfaces in Minkowski 3-space, considering their causal characters, and provides an illustrative example using Mathematica.

Contribution

It introduces the differential equations governing space-like loxodromes on canal surfaces in Minkowski 3-space, considering their causal properties, and demonstrates their application with a computational example.

Findings

Derived differential equations for space-like loxodromes

Analyzed causal characters of canal surfaces

Provided a Mathematica example

Abstract

In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an example by using Mathematica computer programme.