| 摘要: |
| 本文研究了一类重要的形如F=α +εβ +β arctan(β/α) (ε为常数)的弱Berwald (α, β)-度量.利用S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失. |
| 关键词: (α,β)-度量 弱Berwald度量 旗曲率 |
| DOI： |
| 分类号:O186.14 |
| 基金项目:Supported by National Natural Science Foundation of China (10971239); Natural Science Foundation of Guizhou Province (JLKZ201201). |
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| ON A CLASS OF WEAK BERWALD (α, β)-METRICS |
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JIANG Jing-nong1, CHENG Xin-yue2
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1.Department of Medical Information Engineering, Zunyi Medical College, Zunyi 563000, China;2.School of Math. and Statistics, Chongqing University of Technology, Chongqing 400050, China
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| Abstract: |
| We study an important class of weak Berwald (α, β)-metrics in the form F=α + εβ + β arctan(β/α) (ε is a constant) on a manifold. By using a formula of the S-curvature, we obtain sufficient and necessary conditions for such metrics to be weak Berwald metrics. We also prove that F is a weak Berwald metric with scalar flag curvature if and only if it is a Berwald metric and its flag curvature vanishes. |
| Key words: (α, β)-metric weak Berwald metric flag curvature |
