Marginally trapped meridian surfaces of parabolic type in the four-dimensional Minkowski space

TL;DR

This paper classifies and constructs marginally trapped meridian surfaces of parabolic type in four-dimensional Minkowski space, providing explicit geometric descriptions and invariants for these lightlike mean curvature vector surfaces.

Contribution

It introduces a new class of meridian surfaces of parabolic type in Minkowski space and characterizes all marginally trapped examples with explicit invariants.

Findings

Complete classification of marginally trapped meridian surfaces of parabolic type.

Explicit geometric construction of these surfaces.

Derivation of their basic invariants.

Abstract

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their basic invariants. We find all marginally trapped meridian surfaces of parabolic type and give a geometric construction of these surfaces.