| 刘丽红,陈光祖.具有可反测地线的$(\alpha,\beta)$-度量[J].数学研究及应用,2016,36(5):568~574 |
| 具有可反测地线的$(\alpha,\beta)$-度量 |
| On $(\alpha,\beta)$-Metrics with Reversible Geodesics |
| 投稿时间：2015-10-01 修订日期：2016-01-13 |
| DOI：10.3770/j.issn:2095-2651.2016.05.008 |
| 中文关键词: $(\alpha,\beta)$-度量 测地系数 可反的测地线 Douglas曲率 |
| 英文关键词:$(\alpha,\beta)$-metric geodesic coefficient reversible geodesic Douglas curvature |
| 基金项目:国家自然科学基金(Grant No.11471246), 江西省科技厅青年项目(Grant No.20161BAB211021). |
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| 中文摘要: |
| 本文我们得到了$(\alpha,\beta)$-度量的测地系数$G^{i}(x,y)$和其逆$G^{i}(x,-y)$有相同Douglas曲率的充分必要条件.这个充分必要条件恰好是$(\alpha,\beta)$-度量具有可反测地线的充分必要条件. |
| 英文摘要: |
| In this paper, we get necessary and sufficient conditions for a Finsler space endowed with an $(\alpha,\beta)$-metric where its geodesic coefficients $G^{i}(x,y)$ and the reverse of geodesic coefficients $G^{i}(x,-y)$ have the same Douglas curvature. They are the conditions such that $(\alpha,\beta)$-metrics have reversible geodesics. |
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