Abstract
In this paper, we first study two significant non-Riemannian quantities Ξ-curvature and H-curvature and show that a Kropina metric is of almost vanishing Ξ-curvature or H-curvature if and only if it is of isotropic S-curvature. Further, we prove that a Kropina metric F is a Douglas metric if and only if the conformally related metric F˜=eκ(x)F is also Douglas metric. Finally, we classify the Kropina metrics with related isotropic weak Landsberg curvature.
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