A method for designing involute trajectory timelike ruled surfaces in Minkowski 3-space

TL;DR

This paper introduces a novel method for generating involute trajectory timelike ruled surfaces in Minkowski 3-space, focusing on their developability and geometric properties using Lorentzian angles.

Contribution

It presents new theoretical results and theorems on the developability of involute trajectory timelike ruled surfaces in Minkowski 3-space.

Findings

Derived conditions for developability of the surfaces

Presented new theorems related to surface geometry

Provided an illustrative example of the surfaces

Abstract

The aim of this paper is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. Involute trajectory ruled surfaces generated by the Frenet trihedron, moving along spacelike involutes of a given timelike space curve, is stated according to Lorentzian timelike angle between tangent vector and unit vector of direction Darboux vector of this timelike space curve. Also some new results and theorems related to the developability of the involute trajectory timelike ruled surfaces are obtained. Finally we illustrate these surfaces by presenting one example.