对偶平坦和共形平坦的(α,β)-度量(英文)  

ON DUALLY FLAT AND CONFORMALLY FLAT(α, β)-METRICS

作　　者：程新跃[1] 张婷[1] 袁敏高 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《数学杂志》2014年第3期417-422,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10971239)

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.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.

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 

分 类 号：O186.1[理学—数学]