一类具有标量旗曲率的Berwald(α,β)-度量(英文)  

A Class of Weak Berwald (α,β)-metrics With Scalar Flag Curvature

作　　者：汤冬梅[1,2] 

机构地区：[1]厦门理工学院数理系,福建厦门361024 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《数学进展》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)

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.

关 键 词：(Α Β)-度量 S曲率 弱Berwald度量 平均Landsberg曲率 期曲率 

分 类 号：O186[理学—数学]