一类对偶平坦的黎曼度量  

A Class of Dually Flat Riemannian Metrics

作　　者：田艳芳[1] 杨秀文[1] 林琼[1] 徐维[2] 

机构地区：[1]后勤工程学院基础部,重庆401311 [2]后勤工程学院后勤信息与军事物流工程系,重庆401311

出　　处：《后勤工程学院学报》2014年第2期61-64,共4页Journal of Logistical Engineering University

基　　金：国家自然科学基金项目(11371386);贵州省科学技术基金项目(黔科合J字KZL[2012]01号)

摘　　要：给出了黎曼度量局部对偶平坦的一个充分条件:黎曼度量的Spray所满足的方程。同时,指出该条件是非必要的,并给出了相关反例。进一步,对满足条件的这类黎曼度量的性质进行了研究。具体地,讨论了这类度量成为Einstein度量的条件。从黎曼曲率着手,通过计算发现:当空间维数n3,这类黎曼度量是Einstein度量,当且仅当它是欧氏度量;但是,这个结论对n=2的情形不适用。In this paper, a sufficient condition of locally dual flat in Riemannian space is obtained：an equation that the spray of a Riemannian metric satisfies. At the same time, the theory what this condition is not necessary is pointed out since an example is given to prove. Further research is finished to characterize the quality of this kind of Riemannian metrics. The equivalent condition that this kind of locally dually flat Riemannian metric is Einstein metrics is disussed. The quality of this kind of locally dually flat Riemannian metric is been researched to show that they are Einstein metrics. Here Riemannian curvature is main consideration. A series of computation shows that a locally dually flat Riemannian metric is Einstein metric if and only if it is Euclidian with dimen-sion n≥3 . But this is not suitable for the space with dimension n=2.

关 键 词：黎曼度量 局部对偶平坦 爱因斯坦度量 

分 类 号：O186.1[理学—数学]