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

López Camino, Rafael

doi:10.1007/s00022-025-00771-8

s00022-025-00771-8.pdf (329.8Kb)

Identificadores

URI: https://hdl.handle.net/10481/106379

DOI: 10.1007/s00022-025-00771-8

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Editorial

Springer

Materia

General helix

Helix

Lancret relation

Date

2025-08-22

Referencia bibliográfica

López, R. A note on helices in the Euclidean space and in the hyperbolic space. J. Geom. 116, 31 (2025). https://doi.org/10.1007/s00022-025-00771-8

Sponsorship

Universidad de Granada / CBUA (Open access); MINECO/MICINN/FEDER (grant no. PID2023-150727NB-I00); MCINN/AEI/10.13039/ 501100011033/CEX2020-001105-M

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 H3, we obtain the parametrizations of helices for all types of Killing vector fields. It is proved that these helices are geodesics in suitable surfaces of H3.

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