Timelike Loxodromes on Lorentzian Helicoidal Surfaces in Minkowski n--Space (Accepted)


Demirci B. B. , Babaarslan M. , Öge Z.

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics , vol.0, no.0, pp.1-10, 2022 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 0 Issue: 0
  • Publication Date: 2022
  • Title of Journal : Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
  • Page Numbers: pp.1-10

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.