English

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 CC for which there is an FF-constant vector field WW along CC that forms a constant angle with a fixed direction VV (called an axis of the helix). We find the natural equation and the geometric integration of helices CC where the FF-constant vector field WW is orthogonal to its axis.

Keywords

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}
}