Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

Year 2022, Volume: 71 Issue: 3, 856 - 869, 30.09.2022

Burcu Bektaş Demirci , Murat Babaarslan , Zehra Öge

https://doi.org/10.31801/cfsuasmas.1007599

Abstract

In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces
in Minkowski $n$-space.
First, we obtain the first order ordinary differential equations which determine timelike loxodromes
on the Lorentzian helicoidal surfaces in $E_1^n$
according to the causal characters of their meridian curves.
Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes.
In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right
helicoidal surfaces in $E_1^n$. Finally, we give an example to visualize the results.

Keywords

Loxodromes (rhumb lines), navigation, rotational surfaces, helicoidal surfaces, Minkowski space

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