具有标量旗曲率的闵可夫斯基积芬斯勒度量  

Minkowskian Product Finsler Metric with Scalar Flag Curvature

作　　者：田畅 何勇[1] 李淑雯 张辉 TIAN Chang;HE Yong;LI Shu-wen;ZHANG Hui(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）》2022年第3期55-63,共9页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：国家自然科学基金(11761069)。

摘　　要：设(M_(1),F_(1))和(M_(2),F_(2))是两个芬斯勒流形,闵可夫斯基积芬斯勒度量是乘积流形M=M_(1)×M_(2)上赋予的芬斯勒度量F=√f(S,T),其中S=F^(2)_(1),T=F^(2)_(2),且f是积函数。文章推导出F的黎曼曲率系数和旗曲率公式;若F_(1)和F_(2)的旗曲率均消失,得到了F的旗曲率消失的充要条件;当F_(1)和F_(2)具有标量旗曲率时,给出了F仍具有标量旗曲率的微分方程刻画。Let(M_(1),F_(1))and(M_(2),F_(2))be two Finsler manifolds,Minkowskian product Finsler metric is the Finsler metric F=√f(S,T)endowed on the product manifold,M=M_(1)×M_(2) where S=F^(2)_(1),T=F^(2)_(2),f is product function.In this paper,we deduce the Riemannian curvature coefficients and flag curvature formula of F.We give a sufficient and necessary condition for the flag curvature of F vanishes when the flag curvatures of F_(1) and F_(2) vanish.Under the condition that F_(1) and F_(2) are of scalar flag curvature,we give equations to characterize F to be of scalar flag curvature.

关 键 词：闵可夫斯基积 芬斯勒度量 旗曲率 标量旗曲率 

分 类 号：O186.1[理学—数学]