Timelike Loxodromes on Lorentzian Helicoidal Surfaces in Minkowski n--Space
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.71, no.3, pp.856-869, 2022 (ESCI, TRDizin)
- Publication Type: Article / Article
- Volume: 71 Issue: 3
- Publication Date: 2022
- Doi Number: 10.31801/cfsuasmas.1007599
- Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
- Journal Indexes: Emerging Sources Citation Index (ESCI), MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.856-869
- Keywords: Loxodromes (rhumb lines), navigation, rotational surfaces, helicoidal surfaces, Minkowski space
- Yozgat Bozok University Affiliated: Yes
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 $\mathbb{E}^n_1$ 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 $\mathbb{E}^n_1$. Finally, we give an example to visualize the results.