| 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.
|
| Fund Project:the National Natural Science Foundation of China (No.10671214); the Science Foundation of Chongqing Education Committee (No.KJ080620). |
|
| Hits: 3042 |
| Download times: 3143 |
| 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 |
| View Full Text View/Add Comment |
