| 程新跃,鲁从银.两类具有标量旗曲率的弱Berwald度量[J].数学研究及应用,2009,29(4):607~614 |
| 两类具有标量旗曲率的弱Berwald度量 |
| Two Kinds of Weak Berwald Metrics of Scalar Flag Curvature |
| 投稿时间：2007-05-24 修订日期：2007-11-22 |
| DOI：10.3770/j.issn:1000-341X.2009.04.005 |
| 中文关键词: 芬斯勒度量 (\alpha,\beta)-度量 弱Berwald度量 Berwald度量 旗曲率. |
| 英文关键词:Finsler metric ($\alpha,\beta$)-metric weak Berwald metric Berwald metric flag curvature. |
| 基金项目:国家自然科学基金(No.10671214); 重庆市教委科学技术研究项目(KJ080620). |
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| 中文摘要: |
| 本文研究了两类形如$F=\alpha \varepsilon\beta k\beta^2/\alpha$ (其中$\epsilon$和$k\neq 0$是常数)和$F=\alpha^2/(\alpha-\beta)$的具有标量旗曲率的$(\alpha,\beta)$-度量.我们证明了这两类度量是弱Berwald度量的充分必要条件是它们为Berwald度量且其旗曲率为零.此时,这两类度量为局部Minkowski度量. |
| 英文摘要: |
| 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. |
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