In this paper, we study the （α,β）-metrics of scalar flag curvature in the form of F = α ＋ εβ ＋ κβ^2/α （ε and k ≠ 0 are constants） and F = α^2/α-β. We prove that these two kinds of metrics are weak...In this paper, we study the （α,β）-metrics of scalar flag curvature in the form of F = α ＋ εβ ＋ κβ^2/α （ε and k ≠ 0 are constants） and F = α^2/α-β. We prove that these two kinds of metrics are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish. In this case, the metrics are locally Minkowskian.展开更多
基金the National Natural Science Foundation of China(No.10671214)the Science Foundation of Chongqing Education Committee(No.KJ080620)
文摘In this paper, we study the （α,β）-metrics of scalar flag curvature in the form of F = α ＋ εβ ＋ κβ^2/α （ε and k ≠ 0 are constants） and F = α^2/α-β. We prove that these two kinds of metrics are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish. In this case, the metrics are locally Minkowskian.
