On singular square metrics with vanishing Douglas curvature

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.

12 pages, 2 figures