摘要
本文研究了一类具有F=α+εβ+kα~2/β形式的Finsler度量,其中α=(aijy^iy^j)^(1/2)是Riemann度量,β=b_iy^i是非零1-形式,ε和k≠0是常数。得到了这个Finsler度量的S曲率消失和成为弱Berwald度量的充要条件。另外通过证明发现具有标量期曲率的Finsler度量成为弱Berwald度量的充要条件是它们成为Berwald度量,并且期曲率消失。在这种情况下,该Finsler度量就是局部Minkowski度量。
In the present paper,we treat a class of Finsler metrics in the form F =α＋εβ＋κ（α~2/β,where α=（aijy^iy^j）^（1/2）is a Riemann metric,β= biy^i is a nonzero 1-form,and e andκ≠0 are constants.We obtain the sufficient and necessary conditions for F to be vanishing S curvature and weak Berwald metrics.Moreover,it is proved that F with scalar flag curvature are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish.In this case,the metrics are locally Minkowskian.
出处
《数学进展》
CSCD
北大核心
2012年第2期199-208,共10页
Advances in Mathematics（China）
基金
supported in part by NSFC(No.10601040,No.10971170)
Scientific Research Foundation of Xiamen University of Technology(No.YKJ10007R)
