  In this paper, the Cartan tensors of the $(\alpha,\beta)$-norms are
investigated in details. Then an equivalence theorem of $(\alpha,\beta)$-norms
is proved. As a consequence in Finsler geometry, general
$(\alpha,\beta)$-metrics on smooth manifolds of dimension $n\geq4$ with
vanishing Landsberg curvatures must be Berwald manifolds.
