| 两类具有标量旗曲率的弱Berwald度量 |
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| 引用本文： | 程新跃,鲁从银.两类具有标量旗曲率的弱Berwald度量[J].数学研究与评论,2009,29(4):607-614. |
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| 作者姓名： | 程新跃 鲁从银 |
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| 作者单位： | 西南大学数学与统计学院, 重庆 400715; 重庆工学院数理学院, 重庆 400050;重庆大学数理学院, 重庆 400044 |
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| 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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| 摘 要： | 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.
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| 关 键 词： | 标记曲率 度量 弱化 数学分析 |
| 收稿时间： | 2007/5/24 0:00:00 |
| 修稿时间： | 2007/11/22 0:00:00 |
Two Kinds of Weak Berwald Metrics of Scalar Flag Curvature |
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| CHENG Xin Yue and LU Cong Yin.Two Kinds of Weak Berwald Metrics of Scalar Flag Curvature[J].Journal of Mathematical Research and Exposition,2009,29(4):607-614. |
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| Authors: | CHENG Xin Yue and LU Cong Yin |
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| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;School of Mathematics and Physics, Chongqing University of Technology, Chongqing 400050, China
2. Department of Mathematics and Physics, Chongqing University, Chongqing 400044, China |
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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. |
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| Keywords: | Finsler metric ($\alpha \beta$)-metric weak Berwald metric Berwald metric flag curvature |
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