Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-space with Neutral Metric

TL;DR

This paper classifies specific Lorentz surfaces called meridian surfaces in four-dimensional pseudo-Euclidean space, focusing on those with minimal, quasi-minimal, or constant mean curvature, enriching the understanding of their geometric properties.

Contribution

It provides a complete classification of minimal, quasi-minimal, and constant mean curvature meridian surfaces in pseudo-Euclidean 4-space with neutral metric.

Findings

Complete classification of minimal meridian surfaces.

Classification of quasi-minimal meridian surfaces.

Identification of meridian surfaces with non-zero constant mean curvature.

Abstract

In the present paper we consider a special class of Lorentz surfaces in the four-dimensional pseudo-Euclidean space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis and call them meridian surfaces. We give the complete classification of minimal and quasi-minimal meridian surfaces. We also classify the meridian surfaces with non-zero constant mean curvature.