Quasi--minimal surfaces of pseudo--Riemannian space forms with positive relative nullity

TL;DR

This paper classifies quasi-minimal surfaces with positive relative nullity in 4-dimensional pseudo-Riemannian space-forms, revealing their geometric properties and contributing to the understanding of such surfaces in differential geometry.

Contribution

It provides a classification of quasi-minimal surfaces with positive relative nullity in pseudo-Riemannian space-forms, expanding the geometric understanding of these surfaces.

Findings

Geometric properties of surfaces with positive relative nullity

Classification results for quasi-minimal surfaces

Insights into the structure of pseudo-Riemannian space-forms

Abstract

In this paper, we consider surfaces in 4--dimensional pseudo--Riemannian space--forms with index 2. First, we obtain some of geometrical properties of such surfaces considering their relative null space. Then, we get classifications of quasi--minimal surfaces with positive relative nullity.