Rigidity Theorems of Some Dually Flat Finsler Metrics and Its Applications

Abstract

Abstract. In this paper, we study a class of Finsler metric. First, we find some rigidity results of the dually flat (α, β)-metric where the underline Riemannian metric α satisfies nonnegative curvature properties. We give a new geometric approach of the Monge-Ampére type equation on R n by using those results. We also get the non-existence of the compact globally dually flat Riemannian manifold.