共形相关的Matsumoto度量  

On Conformally Related Matsumoto Metrics

作　　者：蒋经农[1] 田艳芳[2] 汪益川[3] 

机构地区：[1]遵义医学院医学信息工程系,贵州遵义563000 [2]后勤工程学院基础部,重庆401311 [3]后勤工程学院科研部,重庆401311

出　　处：《后勤工程学院学报》2012年第5期93-96,共4页Journal of Logistical Engineering University

基　　金：贵州省科学技术基金资助项目(黔科合体R字[2011]2006号)

摘　　要：利用Matsumoto度量F和Fˉ的共形相关性,得到它们一些基本量之间的关系。根据Berwald度量曲率性质,得到它们具有相同Berwald曲率的充分必要条件。进一步,如果度量F为Berwald度量,通过Berwald度量曲率性质,得到Fˉ为Berwald度量的充分必要条件。最后在F为Douglas度量的情形下,通过同样的方法得到Fˉ为Douglas度量的充分必要条件。By using the properties of conformally related Matsumoto metrics F and F, the relationship among some fundamen- tal quantities of both metrics are obtained. According to the curvature properties of Berwald metrics, the sufficient and necessary conditions for conformally related Matsumoto metrics F and F to have the same Berwald curvature are obtained. Further, if F is Berwald metric, by using the curvature properties of Berwald metrics, the sufficient and necessary conditions are obtained for the metric F to be Berwald metric. At last, by the same method, under the condition that F is Douglas metric, the sufficient and necessary con- ditions are obtained for the metric F to be Douglas metric.

关 键 词：芬斯勒度量 Matsumoto度量 共形相关 Berwald曲率 Douglas度量 

分 类 号：O186.1[理学—数学]