Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:71 Issue:3
Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space

Authors : Burcu BEKTAŞ DEMİRCİ, Murat BABAARSLAN, Zehra ÖGE

Pages : 856-869

Doi:10.31801/cfsuasmas.1007599

View : 15 | Download : 11

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski n n -space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in E n 1 E1n 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 n 1 E1n . Finally, we give an example to visualize the results.
Keywords : Loxodromes rhumb lines, navigation, rotational surfaces, helicoidal surfaces, Minkowski space

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