Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space
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Date
2022
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Journal ISSN
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Publisher
Ankara Üniversitesi
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
n
1
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
. Finally, we give an example to visualize the results.
Description
Keywords
Loxodromes (rhumb lines), navigation, rotational surfaces, helicoidal surfaces, Minkowski space