Spacelike Loxodromes on Helicoidal Surfaces in Lorentzian n--Space

TL;DR

This paper investigates the parametrizations and classifications of spacelike loxodromes on helicoidal surfaces in Lorentzian n-space, considering both spacelike and timelike cases, advancing the geometric understanding of these surfaces.

Contribution

It provides explicit parametrizations and classifications of spacelike loxodromes on helicoidal surfaces in Lorentzian n-space, covering both spacelike and timelike types.

Findings

Parametrizations of spacelike loxodromes on spacelike helicoidal surfaces.

Classification of spacelike loxodromes on timelike helicoidal surfaces.

Extension of loxodrome analysis to Lorentzian n-space.

Abstract

In this paper, we study three types of helicoidal surfaces in a Lorentzian n--space $\mathbb{E}^n_1$. First, we find the parametrizations of spacelike loxodromes on such spacelike helicoidal surfaces in $\mathbb{E}^n_1$. Then, we make a similar classification for spacelike loxodromes on such timelike helicoidal surfaces of a Lorentzian n--space $\mathbb{E}^n_1$.