On Slant Helices and General Helices in Euclidean n-Space

TL;DR

This paper explores the relationships between slant helices, spherical helices, and geodesic curves in Euclidean n-space, revealing that slant helices and their tangent indicatrices share the same axis and establishing key geometric connections.

Contribution

It provides new insights into the geometric properties and relations of slant helices and spherical helices in Euclidean n-space, including axis sharing and connections to geodesic curves.

Findings

Slant helices and their tangent indicatrices have the same axis.

Relations between slant helices, spherical helices, and geodesic curves are established.

New geometric characterizations of helices in Euclidean n-space.

Abstract

In this paper, in Euclidean n -space, we investigate the relation between slant helices and spherical helices. Moreover, in E n, we show that a slant helix and the tangent indicatrix of the slant helix have the same axis (or direction). Also, we give the important relations between slant helices, spherical helices in E n and geodesic curves on a helix hypersurface in E n.