Some Theorems on Timelike Ruled Surfaces

TL;DR

This paper explores the existence and properties of timelike ruled surfaces in Minkowski 3-space, providing general theorems based on curvature, distribution parameter, and special cases like geodesics and helices.

Contribution

It presents new existence theorems for timelike ruled surfaces considering various geometric conditions and special cases, expanding understanding in Minkowski geometry.

Findings

Existence theorems for timelike ruled surfaces based on curvature and other parameters

Characterization of surfaces with geodesic, asymptotic line, or helix directrix

Special cases illustrating the general theory

Abstract

In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike ruled surface according to Gaussian curvature, distribution parameter and strictional distance. Moreover, we give some special cases such as the directirx of the surface is a geodesic, an asymptotic line, a line of curvature or a general helix.