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

In this paper we study the flag curvature of a new class of Finsler metrics called general (α,β)(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 locally projectively flat. As a result, we construct many new projectively flat Finsler metrics with flag curvature 1, 0 and −1 in Section 9, all of which are of singularity at some directions.