Marginally trapped surfaces with pointwise 1-type Gauss map in Minkowski 4-space

TL;DR

This paper classifies marginally trapped surfaces in Minkowski 4-space that have a pointwise 1-type Gauss map, showing they are characterized by having a parallel mean curvature vector field.

Contribution

It provides a complete characterization of marginally trapped surfaces with pointwise 1-type Gauss map in Minkowski space, linking this property to parallel mean curvature vectors.

Findings

All such surfaces have parallel mean curvature vectors.

A marginally trapped surface has pointwise 1-type Gauss map iff it has parallel mean curvature vector.

The paper offers a classification of these surfaces in Minkowski 4-space.

Abstract

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if and only if it has parallel mean curvature vector field.