Space-like Surfaces in Minkowski Space $\mathbb E^4_1$ with Pointwise 1-Type Gauss Map

TL;DR

This paper classifies space-like surfaces in Minkowski, de-Sitter, and hyperbolic spaces based on their harmonic and pointwise 1-type Gauss maps, providing characterizations, classifications, and explicit examples.

Contribution

It offers a comprehensive classification of space-like surfaces with harmonic and pointwise 1-type Gauss maps in various Lorentzian manifolds, including explicit examples.

Findings

Classified space-like surfaces with harmonic Gauss map in Minkowski, de-Sitter, and hyperbolic spaces.

Characterized and classified space-like surfaces with pointwise 1-type Gauss map of the first kind.

Provided explicit examples of such surfaces.

Abstract

In this work we firstly classify space-like surfaces in Minkowski space $\mathbb E^4_1$, de-Sitter space $\mathbb S^3_1$ and hyperbolic space $\mathbb H^3$ with harmonic Gauss map. Then we give a characterization and classification of space-like surfaces with pointwise 1-type Gauss map of the first kind. We also give some explicit examples.