Similar Ruled Surfaces with Variable Transformations in Minkowski 3-space

TL;DR

This paper explores the properties of similar ruled surfaces in Minkowski 3-space, establishing conditions under which developable, cylindrical, and conoid surfaces are similar, based on their striction curves and transformations.

Contribution

It introduces the concept of similar ruled surfaces with variable transformations in Minkowski 3-space and characterizes their properties and relationships.

Findings

Developable ruled surfaces form a family of similar surfaces if their striction curves are similar with variable transformation.

Cylindrical surfaces and conoids constitute two families of similar ruled surfaces in Minkowski 3-space.

The study provides conditions for similarity based on the geometry of striction curves.

Abstract

In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3 form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation. Moreover, we obtain that cylindrical surfaces and conoids form two families of similar ruled surfaces in E_1^3.