Berwald双挠积Finsler度量  

Berwald Doubly-Twisted Product Finsler Metric

作　　者：邓香香 何勇[1] 张娜 DENG Xiang-xiang;HE Yong;ZHANG Na(College of Mathematical Sciences,XinJiang Normal University,Urumqi,XinJiang,830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《新疆师范大学学报（自然科学版）》2021年第2期10-16,共7页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：国家自然科学基金(11761069)。

摘　　要：设F_(1)和F_(2)是两个Finsler度量,f_(1)和f_(2)是乘积流形M=M_(1)×M_(2)上的非负光滑函数,双挠积Finsler度量是在乘积流形上赋予的Finsler度量F_(2)=f_(2)_(2)F_(1)^(2)+f_(1)^(2)F_(2)^(2).文章首先推导出双挠积Finsler度量的Berwald联络系数,其次给出了双挠积Finsler度量的Berwald曲率系数公式,最后得到双挠积Finsler度量是Berwald度量的充要条件,并证明了具有迷向Berwald曲率的双挠积Finsler度量是Berwald度量。Let F_(1) and F_(2) be two Finsler metrics.The doubly twisted product Finsler metrics is the product manifold M=M_(1)×M_(2) endowed with the twisted product Finsler metric F_(2)=f_(2)_(2)F_(1)^(2)+f_(1)^(2)F_(2)^(2),where f_(1) and f_(2) are positive smooth functions on M_(1)×M_(2).In this paper,the Berwald connection coefficient doubly-twisted product of Finsler metric is deduced.Secondly,the Berwald curvature coefficient formula doubly-twisted product of Finsler met⁃ric is given.Finally,the necessary and sufficient conditions for a doubly-twisted product of Finsler metric to be a Berwald metric is abtained.And it is proved that the doubly-twisted product of Finsler metric with isotropic Berwald curvature is Berwald metric.

关 键 词：FINSLER度量 双挠积 Berwald度量 Berwald曲率 迷向Berwald曲率 

分 类 号：O186.1[理学—数学]