An equivalence theorem of a class of Minkowski norms and its applications

Abstract

In this paper, the Cartan tensors of the (α, β)-norms are investigated in detail. Then an equivalence theorem of (α, β)-norms is proved. As a consequence in Finsler geometry, general (α, β)-metrics on smooth manifolds of dimension n ⩾ 4 with vanishing Landsberg curvatures must be Berwald manifolds.