On Riemann curvature of singular square metrics

TL;DR

This paper establishes necessary and sufficient conditions for singular square Finsler metrics to have constant Ricci or flag curvature in dimensions three and higher, advancing understanding of their geometric properties.

Contribution

It provides the first complete characterization of constant curvature conditions for singular square metrics, a special class of non-regular Finsler metrics.

Findings

Derived necessary and sufficient conditions for constant Ricci curvature.

Derived necessary and sufficient conditions for constant flag curvature.

Extended curvature analysis to non-regular Finsler metrics in higher dimensions.

Abstract

Square metrics is an important class of Finsler metrics. Recently, we introduced a special class of non-regular Finsler metrics called singular square metrics. The main purpose of this paper is to provide a necessary and sufficient condition for singular square metrics to be of constant Ricci or flag curvature when dimension $n\geq3$.