A generalization of the notion of helix
Differential Geometry
2026-01-27 v1
Abstract
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve for which there is an -constant vector field along that forms a constant angle with a fixed direction (called an axis of the helix). We find the natural equation and the geometric integration of helices where the -constant vector field is orthogonal to its axis.
Cite
@article{arxiv.2601.18020,
title = {A generalization of the notion of helix},
author = {Pascual Lucas and José Antonio Ortega-Yagües},
journal= {arXiv preprint arXiv:2601.18020},
year = {2026}
}