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A class of Finsler metrics with almost vanishing H-curvature

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known in the case of metrics with vanishing H-curvature. M.S.C. 2010: 58E20, 53B40.