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In this paper, we define a new projective invariant and call it W-curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W-curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.fatcat:22vj2a4565bzhhhqytsb6azbua