Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise 1-type Gauss Map in Minkowski 4-Space

TL;DR

This paper classifies certain spacelike surfaces in Minkowski 4-space based on their Gauss map properties, specifically focusing on meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map.

Contribution

It provides a complete classification of meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space.

Findings

Identified all meridian surfaces with harmonic Gauss map.

Classified meridian surfaces with pointwise 1-type Gauss map.

Abstract

In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these surfaces with respect to their Gauss map. We find all meridian surfaces of elliptic or hyperbolic type with harmonic Gauss map and give the complete classification of meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map.