What type of study is this?

This is a Quantitative Study study.

October 19, 2025Open Access

A note on helices in the Euclidean space and in the hyperbolic space

Key Points

Helices in euclidean space correspond to curves with constant curvature and constant torsion, revealing their geometric nature.
In hyperbolic space, helices are parametrized for various Killing vector fields, including hyperbolic and spherical rotations.
These helices function as geodesics within specific surfaces in hyperbolic space, showcasing their unique properties.
The findings enhance the understanding of the geometric behavior of helices in different spatial structures.

Abstract

We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space ³, we obtain the parametrization of helices for the Killing vector fields associated to hyperbolic rotations, spherical rotations and parabolic rotations. It is proved that these helices are geodesics in suitable surfaces of ³.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Rafael López (Thu,) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc697015 https://doi.org/https://doi.org/10.48550/arxiv.2507.12861

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Mark Helpful

Bookmark

Relay

View Full Paper