Two Kinds of Weak Berwald Metrics of Scalar Flag Curvature |
Received:May 24, 2007 Revised:November 22, 2007 |
Key Words:
Finsler metric ($\alpha,\beta$)-metric weak Berwald metric Berwald metric flag curvature.
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Fund Project:the National Natural Science Foundation of China (No.10671214); the Science Foundation of Chongqing Education Committee (No.KJ080620). |
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Abstract: |
In this paper, we study the ($\alpha,\beta$)-metrics of scalar flag curvature in the form of $F=\alpha \varepsilon\beta k\frac{\beta^{2}}{\alpha}$ ($\varepsilon $ and $k\neq 0$ are constants) and $F=\frac{\alpha^{2}}{\alpha-\beta}$. 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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2009.04.005 |
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