Narrow Results

In this paper, we establish a closer relation between the Berwald scalar curvature and the $S$-curvature. In fact, we prove that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic $S$-curvature. For Finsler metrics of scalar flag curvature and of weakly isotropic $S$-curvature, they have almost isotropic $S$-curvature if and only if the flag curvature is weakly isotropic.

In the present paper, we prove that a general $(\alpha ,\beta )$-metric $F$ is of isotropic $S$-curvature if and only if it is of isotropic $E$-curvature under an extra condition on $\alpha$ and $\beta$.