On locally dually flat general (α, β)-metrics

Locally flat Finsler metrics arise from information geometry. Some speciel locally dually flat Finsler metrics had been studied in Cheng et al. [3] and Xia [4] respectively. As we konw, a new class of Finsler metrics called general (α, β)-metrics are introduced, which are defined by a Riemannian metrics α and 1-form β. These metrics generalize (α, β)-metrics naturally. In this paper, we give a characterization of locally dually flat general (α, β) -metrics on an n-dimensional mannifold Mn(n ≥ 3), which generalizes some results in Cheng et al. [3] and Xia [4].