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).
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 i...