Some Classification Theorems On (α, β)-Metrics With Scalar Flag Curvature

In this paper, we study some classification of (α,β)-metric with scalar flag curvature. First of all, we consider (α,β)?metrics with scalar flag curvature in the forms of F =α+εβ+ kβ2 /αand F =α2 / (α?β), whereεand k≠0 are constants . We prove that if these two kinds of (α,β)?metrics are of isotropic S-curvatures ,then they are Berwald metrics and of zero flag curvature, namely , they are locally Minkowski metrics. More general, for (α,β)?metrics of non-Randers type with scalar flag curvature, we prove that if these(α,β)?metrics are of vanishing S-curvature, then they are also Berwald metrics and of zero flag curvatures, namely, they are locally Minkowski metrics.