Meridian Surfaces with Parallel Normalized Mean Curvature Vector Field in Pseudo-Euclidean 4-space with Neutral Metric

TL;DR

This paper classifies a special class of Lorentz surfaces in pseudo-Euclidean 4-space with neutral metric, focusing on those with parallel normalized mean curvature vectors, revealing unique geometric properties.

Contribution

It provides a complete classification of meridian surfaces with parallel and normalized mean curvature vectors in pseudo-Euclidean 4-space.

Findings

Existence of Lorentz surfaces with parallel normalized mean curvature vector but not parallel mean curvature vector

Complete classification of meridian surfaces with these properties

Identification of geometric conditions for these surfaces

Abstract

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-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 the meridian surfaces with parallel mean curvature vector field. We also classify the meridian surfaces with parallel normalized mean curvature vector. We show that in the family of the meridian surfaces there exist Lorentz surfaces which have parallel normalized mean curvature vector field but not parallel mean curvature vector.