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 β۲/α , where α is Riemannian metric, β is a ۱-form, and ε,k(≠ ۰) are constant. We give a complete classification for such metrics to be locally dually flat. By assumption β is a conformal ۱-form, we show that the metric is locally dually flat if and only if α is a Euclidean metric and β is a constant ۱-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.

Keywords:

Finsler metric , (α , β)- metric , locally dually flat