On singular square metrics with vanishing Douglas curvature

TL;DR

This paper characterizes singular square Finsler metrics with vanishing Douglas curvature and provides analytical examples using $eta$-deformations, advancing understanding of their geometric properties.

Contribution

It offers a characterization of singular square metrics with zero Douglas curvature and constructs explicit examples through $eta$-deformations.

Findings

Characterization of singular square metrics with vanishing Douglas curvature

Construction of analytical examples via $eta$-deformations

Enhanced understanding of geometric properties of these metrics

Abstract

Square metrics $F=\frac{(\alpha+\beta)^2}{\alpha}$ are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $F=\frac{(b\alpha+\beta)^2}{\alpha}$. A characterization for such metrics to be of vanishing Douglas curvature is provided. Moreover, many analytical examples are achieved by using a special kinds of metrical deformations called $\beta$-deformations.