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

Abstract

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 $n\ge 4$ with vanishing Landsberg curvatures must be Berwald manifolds.

accepted for publication in SCIENCE CHINA Mathematics

References in corpus (4)

• Finsleroid--Finsler Space with Berwald and Landsberg Conditions
• The Euler-Lagrange PDE and Finsler metrizability
• On the Berwald-Landsberg problem
• On equivalence theorems of Minkowski spaces and applications in Finsler geometry