Two classes of weakly Landsberg Finsler metrics

In this paper, we investigate the mean Landsberg curvature of two subclasses of (α,β)-metrics. We prove that these subclasses of (α,β)-metrics with vanishing mean Landsberg curvature have vanishing S-curvature. Using it, we prove that these Finsler metrics are weakly Landsbergian if and only if they are Berwaldian.

Keywords:

weakly Landsberg metric , (α , β)-metric , S-curvature