Glasnik Matematicki, Vol. 60, No. 1 (2025), 147-165. \( \)

SPHERICAL GENERALIZED HELICES IN 3-DIMENSIONAL LORENTZ-MINKOWSKI SPACE

Ivana Filipan, Željka Milin Šipuš and Ljiljana Primorac Gajčić

Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:ivana.filipan@rgn.unizg.hr

Department of mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:milin@math.hr

School of Applied Mathematics and Informatics, University of Osijek, 31 000 Osijek, Croatia
e-mail:ljiljana.primorac@mathos.hr

Abstract.   In this paper we analyze generalized helices lying on the non-degenerated quadric surfaces in 3-dimensional Lorentz-Minkowski space, i.e. on a pseudosphere and in a hyperbolic plane. We provide their characterizations in terms of curvature and torsion and analyze their projections onto planes orthogonal to their axes. We show that these projections appear as Euclidean or Lorentzian cycloidal curves, so we also introduce natural equations and parametrizations of Lorentzian cycloidal curves.

2020 Mathematics Subject Classification.   53A35, 53B30

Key words and phrases.   Lorentz-Minkowski space, generalized helix, spherical curve, cycloidal curve.

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.60.1.09

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