On a special class of dually flat (α, β)-metrics

In this paper, we first study a special class of (α,β)-metrics in the form f = α + εβ + k β2/α , where α is riemannian metric, β is a 1-form, and ε,k(≠ 0) are constant. we give a complete classification for such metrics to be locally dually flat. by assumption β is a conformal 1-form, we show that the metric is locally dually flat if and only if α is a euclidean metric and β is a constant 1-form. further, we classify locally dually flat of a class of finsler metric in the form f = α exp( α/β ) + εβ, where ε is constant.