On rotational surfaces with zero mean curvature in the pseudo-Euclidean space $\mathbb{E}_2^4$

TL;DR

This paper investigates rotational surfaces with zero mean curvature in the pseudo-Euclidean space $ extbf{E}_2^4$, providing explicit parametrizations and solutions to the differential equations governing such surfaces.

Contribution

It introduces explicit parametrizations and solutions for maximal and timelike rotational surfaces with zero mean curvature in $ extbf{E}_2^4$, expanding understanding of these geometric structures.

Findings

Explicit parametrizations of maximal rotational surfaces.

Solutions to differential equations for zero mean curvature surfaces.

Characterization of timelike surfaces with zero mean curvature.

Abstract

In this work, we study a class of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}_2^4$ whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero mean curvature to determine the profile curves of such rotational surfaces. Then, we give some explicit parametrization of maximal rotational surfaces and the timelike surfaces with zero mean curvature in $\mathbb{E}_2^4$.