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.
Categories: math.DG math.MG