The natural equations of three-dimensional helices

Abstract In this paper we use the notion of helix associated to a F -constant vector field, which has cylindrical and slant helices as particular examples, to find its natural equation. In the case of normal helices, we prove that they are characterized by being the pseudo-geodesics of helix surfaces.

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Publication Details

Journal
Journal of Geometry
Published
2026-01-21
DOI
https://doi.org/10.1007/s00022-026-00793-w
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
Field-Weighted Citation Impact
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article

The natural equations of three-dimensional helices

Pascual García Lucas, José Antonio Ortega-Yagües
Journal of Geometry
Geometric Analysis and Curvature Flows
article

The natural equations of three-dimensional helices

Pascual García Lucas, José Antonio Ortega-Yagües
article en

Abstract

Abstract In this paper we use the notion of helix associated to a F -constant vector field, which has cylindrical and slant helices as particular examples, to find its natural equation. In the case of normal helices, we prove that they are characterized by being the pseudo-geodesics of helix surfaces.

Journal of GeometryVol. 117(1)
Openalex Percentile: Top 78%
Geometric Analysis and Curvature Flows
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The natural equations of three-dimensional helices — Pascual García Lucas, José Antonio Ortega-Yagües · Journal of Geometry (2026) | TGRS Research Map | TGRS