Characterizations of special skew ruled surfaces by the normal curvature of some distinguished families of curves

TL;DR

This paper classifies skew ruled surfaces in 3D space based on the specific forms of normal curvature of certain distinguished curves, providing a comprehensive characterization of these geometric structures.

Contribution

It introduces a complete classification of skew ruled surfaces with prescribed normal curvature properties for special families of curves.

Findings

Identifies all skew ruled surfaces with given normal curvature conditions.

Provides explicit characterizations of these surfaces.

Enhances understanding of the geometry of ruled surfaces.

Abstract

We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled surfaces with the mentioned property.