On singular square metrics with vanishing Douglas curvature

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Square metrics F=(α+β)²α 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=(bα+β)²α. 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.