Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

TL;DR

This paper investigates the geometric properties of slant ruled surfaces in Euclidean 3-space, deriving differential equations and conditions relating their conical curvatures and associated ruled surfaces.

Contribution

It introduces new differential equations and conditions characterizing slant ruled surfaces and their related surfaces in Euclidean 3-space.

Findings

Derived differential equations for slant ruled surfaces

Established conditions for related ruled surfaces to be slant

Analyzed relationships between conical curvatures and surface vectors

Abstract

In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give some conditions for the surfaces drawn by the central normal and the central tangent vectors to be slant ruled surfaces.