On the non-Riemannian quantity H in Finsler geometry

In this paper, we study a new non-Riemannian quantity H defined by the S-curvature. We find that the non-Riemannian quantity is closely related to S-curvature. We characterize Randers metrics of almost isotropic S-curvature if and only if they have almost vanishing H-curvature. Furthermore, the Randers metrics actually have zero S-curvature if and only if they have vanishing H-curvature.