双挠积复Finsler流形的局部对偶平坦性  

Locally Dually Flatness of Doubly Twisted Product Complex Finsler Manifold

作　　者：肖维 何勇[1] 栗嘉慧 邓香香 XIAO Wei;HE Yong;LI Jiahui;DENG Xiangxiang(School of Mathematical Sciences,Xinjiang Normal University,Urumqi,Xinjiang,830017,P.R.China)

机构地区：[1]新疆师范大学数学科学学院,乌鲁木齐新疆830017

出　　处：《数学进展》2023年第2期371-376,共6页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.12261088,11761069)。

摘　　要：设(M_(1),F_(1))和(M_(2),F_(2))是两个强凸的复Finsler流形,λ_(1)和λ_(2)是乘积流形M=M_(1)×M_(2)上的光滑实值函数,双挠积复Finsler流形(M1×(λ_(1,)λ_(2))M_(2),F)是在乘积流形上赋予了复Finsler度量F^(2)=λ_(1)^(2)F_(1)^(2)+λ_(2)^(2)F_(2)^(2)的复Finsler流形.本文给出了双挠积复Finsler流形是局部对偶平坦流形的充要条件.Let(M_(1),F_(1))and(M_(2),F_(2))be two strongly convex complex Finsler manifolds.The doubly twisted product complex Finsler manifold(MiX(A1,Aa)M2,F)is the product manifold M1×M2 endowed with the twisted product complex Finsler metric F2=F1+2F2,where A1 and X2 are positive smooth functions on M_(1)×M_(2).In this paper,we obtain the necessary and sufficient conditions that the doubly twisted product complex Finsler manifold(Mi x(A1,a)M2,F)is a locally dually flat manifold.

关 键 词：双挠积 复FINSLER流形 局部对偶平坦 

分 类 号：O186.1[理学—数学]