| 摘要: |
| 本文主要研究了对偶平坦和共形平坦的(α,β)-度量.利用对偶平坦和共形平坦与其测地线的关系,得到了局部对偶平坦和共形平坦的Randers度量是Minkowskian度量的结论.进一步,推广到非Randers型的情形,我们证明了局部对偶平坦和共形平坦的非Randers型的(α,β)-度量在附加的条件下一定是Minkowskian度量. |
| 关键词: (α,β)度量 对偶平坦的Finsler度量 共形平坦的Finsler度量 Minkowskian度量 |
| DOI： |
| 分类号:O186.1 |
| 基金项目:Supported by National Natural Science Foundation of China (10971239). |
|
| ON DUALLY FLAT AND CONFORMALLY FLAT(α, β)-METRICS |
|
CHENG Xin-yue, ZHANG Ting, YUAN Min-gao
|
|
School of Math. and Statistics, Chongqing University of Technology, Chongqing 400054, China
|
| Abstract: |
| In this paper, from the relation between the sprays of two dually flat and conformally flat (α, β) -metrics, we obtain that locally dually flat and conformally flat Randers metrics are Minkowskian. Further, we extend the result to the non-Randers type and show that the locally dually flat and conformally flat (α, β)-metrics of non-Randers type must be Minkowskian under an extra condition. |
| Key words: (α, β)-metric dually flat Finsler metric conformally flat Finsler metric, Minkowski metirc |
