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 manifo...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.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11221091, 11271062, 11501067, 11571184, 11871126 and 11931007)China Scholarship Council Visiting Scholar Program+1 种基金the Fundamental Research Funds for the General UniversitiesNankai Zhide Foundation。
文摘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.
