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

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.