On singular square metrics with vanishing Douglas curvature

Square metrics $F=\frac{(α+β)^2}α$ 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 $F=\frac{(bα+β)^2}α$. 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 $β$-deformations.

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