Projectively flat general (α,β)-metrics with constant flag curvature

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In this paper we study the flag curvature of a particular class of Finsler metrics called general (α,β)-metrics, which are defined by a Riemannian metric α and a 1-form β. The classification of such metrics with constant flag curvature are completely determined under some suitable conditions, which make them be locally projectively flat. As a result, we construct some new projectively flat Finsler metrics with flag curvature 1, 0 and -1, all of which are of singularity at some directions.