Isometric Timelike Surfaces in 4--Dimensional Minkowski Space
Burcu Bekta\c{s} Dem\.irc\.i, Murat Babaarslan, Yasin K\"u\c{c}\"ukarikan
TL;DR
This paper investigates isometric timelike surfaces in 4D Minkowski space, exploring Bour's theorem, geometric properties, and parametrizations, with examples and visualizations using Mathematica.
Contribution
It extends Bour's theorem to four types of timelike helicoidal surfaces in 4D Minkowski space and provides explicit parametrizations and examples.
Findings
Bour's theorem is applicable to four types of timelike helicoidal surfaces.
Explicit parametrizations of isometric surfaces are derived.
Examples and visualizations of the surfaces are provided.
Abstract
In this paper, first we study on Bour's theorem for four kinds of timelike helicoidal surfaces in 4-dimensional Minkowski space. Secondly, we analyse the geometric properties of these isometric surfaces having same Gauss map. Also, we present the parametrizations of such isometric pair of surfaces. Finally, we introduce some examples and draw the corresponding graphs by using Wolfram Mathematica 10.4.
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