Quasi-minimal Rotational Surfaces in Pseudo-Euclidean Four-dimensional Space

TL;DR

This paper classifies all quasi-minimal rotational surfaces of elliptic, hyperbolic, and parabolic types in four-dimensional pseudo-Euclidean space with neutral metric, expanding understanding of their geometric properties.

Contribution

It provides a complete classification of quasi-minimal rotational surfaces of all three types in four-dimensional pseudo-Euclidean space.

Findings

Classification of elliptic quasi-minimal rotational surfaces

Classification of hyperbolic quasi-minimal rotational surfaces

Classification of parabolic quasi-minimal rotational surfaces

Abstract

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all quasi-minimal rotational surfaces of elliptic, hyperbolic and parabolic type, respectively.