What question did this study set out to answer?

The aim is to explore the natural equations of helices associated with constant vector fields.

January 25, 2026Journal of GeometryOpen Access

The natural equations of three-dimensional helices

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The aim is to explore the natural equations of helices associated with constant vector fields.
Introduced the concept of helices related to F-constant vector fields.
Examined cylindrical and slant helices as specific cases.
Analyzed normal helices as pseudo-geodesics of helix surfaces.
Demonstrated that normal helices are characterized as pseudo-geodesics on helix surfaces.
Derived the natural equations for different types of helices.

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Implication

Reveals the natural equations of helices in vector fields, suggesting insights into geometric properties.

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.

Cite This Study

Lucas et al. (2026) studied this question.

synapsesocial.com/papers/6975b1eafeba4585c2d6d6cc https://doi.org/10.1007/s00022-026-00793-w

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Implication

Reveals the natural equations of helices in vector fields, suggesting insights into geometric properties.

The natural equations of three-dimensional helices

Key Points

Discussion

Member takes

Implication

Abstract

Cite This Study

The natural equations of three-dimensional helices

Key Points

Discussion

Member takes

Implication

Abstract

Cite This Study