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Glasnik matematički, Vol. 60 No. 1, 2025.

Izvorni znanstveni članak

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

Spherical generalized helices in 3-dimensional Lorentz-Minkowski space

Ivana Filipan orcid id orcid.org/0000-0001-6616-3206 ; Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia
vZeljka Milin vSipuš orcid id orcid.org/0000-0002-0726-3335 ; Department of mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
Ljiljana Primorac Gajčić ; School of Applied Mathematics and Informatics, University of Osijek, 31 000 Osijek, Croatia

Puni tekst: engleski pdf 1.342 Kb

str. 147-165

preuzimanja: 171

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Sažetak

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.

Ključne riječi

Lorentz-Minkowski space, generalized helix, spherical curve, cycloidal curve.

Hrčak ID:

332473

URI

https://hrcak.srce.hr/332473

Datum izdavanja:

26.5.2026.

Posjeta: 428 *

Publication date: 10 June 2025

Volume: Vol 60

Issue: Svezak 1

Pages: 147-165

DOI: 10.3336/gm.60.1.09

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Lorentz-Minkowski space, generalized helix, spherical curve, cycloidal curve.

Spherical generalized helices in 3-dimensional Lorentz-Minkowski space

Ivana Filipan[1]

Email: ivana.filipan@rgn.unizg.hr

vZeljka Milin vSipuš[2]

Email: milin@math.hr

Ljiljana Primorac Gajčić[3]

Email: ljiljana.primorac@mathos.hr

 

[1] Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia

[2] Department of mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia

[3] School of Applied Mathematics and Informatics, University of Osijek, 31 000 Osijek, Croatia

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.

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