Classification of minimal Lorentzian surfaces in $\mathbb S^4_2(1)$ with constant Gaussian and normal curvatures

TL;DR

This paper classifies minimal Lorentzian surfaces in a 4D pseudo-Riemannian sphere with constant Gaussian and normal curvatures, identifying specific curvature values and providing explicit examples.

Contribution

It provides a complete classification of minimal Lorentzian surfaces with constant curvatures in ^4_2(1), including explicit examples and specific curvature values.

Findings

Gaussian curvature is 1/3

Normal curvature's absolute value is 2/3

Explicit examples of such surfaces are given

Abstract

In this paper we consider Lorentzian surfaces in the 4-dimensional pseudo-Riemannian sphere $\mathbb S^4_2(1)$ with index 2 of curvature one. We obtain the complete classification of minimal Lorentzian surfaces $\mathbb S^4_2(1)$ whose Gaussian and normal curvatures are constants. We conclude that such surfaces have the Gaussian curvature $1/3$ and the absolute value of normal curvature $2/3$. We also give some explicit examples.