Timelike Loxodromes on Lorentzian Helicoidal Surfaces in Minkowski n--Space

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Atıf İçin Kopyala

Demirci B. B., Babaarslan M., Öge Z.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.71, sa.3, ss.856-869, 2022 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 71 Sayı: 3
• Basım Tarihi: 2022
• Doi Numarası: 10.31801/cfsuasmas.1007599
• Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.856-869
• Anahtar Kelimeler: Loxodromes (rhumb lines), navigation, rotational surfaces, helicoidal surfaces, Minkowski space
• Yozgat Bozok Üniversitesi Adresli: Evet

Özet

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.