Constant Angle Ruled Surfaces in Euclidean Spaces

TL;DR

This paper investigates constant angle ruled surfaces and helix hypersurfaces in Euclidean spaces, focusing on their geometric properties, developability conditions, and the surfaces generated by plane curves.

Contribution

It introduces new characterizations of ruled surfaces with constant angle properties and explores their developability and generation by plane curves in Euclidean spaces.

Findings

Characterization of constant angle ruled surfaces.

Conditions for developability of these surfaces.

Generation of helix surfaces by plane curves.

Abstract

In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give requirement of being developable of the ruled surface. Also, we investigate the helix surface generated by a plane curve in Euclidean 3-space .