On a Class of Weakly-Berwald （α,β）-Metrics  

作　　者：XIANG Chun Huan CHENG Xin Yue 

机构地区：[1]School of Mathematics and Statistics, Chongqing University of Arts and Sciences, Chongqing 402160, China [2]School of Mathematics and Physics, Chongqing Institute of Technology, Chongqing 400050, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第2期227-236,共10页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China （No. 10671214）; the Natural Science Foundation of Chongqing Education Committee （No. KJ080620）; the Science Foundation of Chongqing University of Arts and Sciences （No. Z2008SJ14）.

摘　　要：In this paper, we study an important class of (α,β)-metrics in the form F = (α + β)m+1/αm on an n-dimensional manifold and get the conditions for such metrics to be weakly-Berwald metrics, where α = aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form and m is a real number with m = 1,0,1/n. Furthermore, we also prove that this kind of (α,β)-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.In this paper, we study an important class of （α,β）-metrics in the form F = （α＋β）^m＋1/α^m on an n-dimensional manifold and get the conditions for such metrics to be weakly- Berwald metrics, where α = √aij（x）y^iy^j is a Riemannian metric and β = bi（x）y^i is a 1-form and m is a real number with m ≠ -1,0,-1/n. Furthermore, we also prove that this kind of （α,β）-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.

关 键 词：mean Berwald curvature weakly-Berwald metric S-CURVATURE （α β）-metric. 

分 类 号：O186.1[理学—数学]