General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric

TL;DR

This paper introduces and classifies various types of general rotational surfaces in pseudo-Euclidean 4-space with neutral metric, focusing on minimal, flat, and special curvature properties.

Contribution

It extends the concept of rotational surfaces to pseudo-Euclidean space and provides a complete classification of surfaces with specific geometric properties.

Findings

Classification of minimal general rotational surfaces

Identification of flat general rotational surfaces

Analysis of surfaces with flat normal connection

Abstract

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classification of minimal general rotational surfaces of elliptic and hyperbolic type, general rotational surfaces with parallel normalized mean curvature vector field, flat general rotational surfaces, and general rotational surfaces with flat normal connection.