Original scientific paper

https://doi.org/10.31896/k.24.4

Generalized Helices on a Lightlike Cone in 3-Dimensional Lorentz-Minkowski Space

Željka Milin Šipuš orcid.org/0000-0002-0726-3335 ; Faculty of Science, University of Zagreb, Zagreb, Croatia
Ivana Protrka orcid.org/0000-0001-6616-3206 ; Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Zagreb, Croatia
Ljiljana Primorac Gajčić orcid.org/0000-0002-8460-3196 ; Department of Mathematics, University of Osijek, Osijek, Croatia

Abstract

In this paper we provide characterizations and give some properties of generalized helices in 3-dimensional Lorentz-Minkowski space that lie on a lightlike cone. Furthermore, by analyzing their projections, which turn out to be Euclidean or Lorentzian logarithmic spiral, we present their parametrizations. In particular, we also analyze planar generalized helices, that is planar intersections of a lightlike cone.

Keywords

Lorentz-Minkowski space; generalized helix; curve of constant slope; lightlike cone

Hrčak ID:

248415

URI

https://hrcak.srce.hr/248415

Publication date:

27.12.2020.

Article data in other languages: croatian

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