两类重要的局部对偶平坦的Douglas(α,β)-度量  

Two important classes of locally dually flat Douglas(α,β)-metrics

作　　者：蒋经农[1] 程新跃[2] 

机构地区：[1]遵义医学院医学信息工程系,贵州遵义563000 [2]重庆理工大学数学与统计学院,重庆400054

出　　处：《兰州理工大学学报》2013年第2期152-155,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10971239);贵州省科学技术基金(黔科合J字LKZ[2012]01号)

摘　　要：研究两类重要的分别形如F=α+εβ+β arctan(β/α)和F=α2/(α-β)+μβ的(α,β)-度量,其中μ≠-1和ε≠0为常数,α=～1/aij(x)yiyj为黎曼度量,β=bi(x)yi为流形上的1-形式.得到它们为局部对偶平坦的Douglas度量的充要条件.Two important classes of （α,β）-metrics in the forms of F=α＋εβ＋βarctan（β/α） and F=α^2（α-β）＋μβ were considered, whereμ≠-1 and ε≠0 were constants, α=√αu（x）yiyi was Riemannianmetric, β=bi（x）yi was a 1-form on a manifold. The sufficient and necessary conditions for them to be locally dually flat Douglas metrics were obtained.

关 键 词：芬斯勒度量 (Α Β)-度量 局部对偶平坦的(α β)-度量 Douglas度量 

分 类 号：O186.1[理学—数学]