On general (alpha,beta)-metrics with vanishing Douglas curvature

In this paper, we study a class of Finsler metrics called general $(α,β)$-metrics, which are defined by a Riemannian metric $α$ and a $1$-form $β$. We find an equation which is necessary and sufficient condition for such Finsler metric to be a Douglas metric. By solving this equation, we obtain all of general $(α,β)$-metrics with vanishing Douglas curvature under certain condition. Many new non-trivial examples are explicitly constructed.

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