A Class of Finsler Metrics with Almost Vanishing H- and $$\Xi $$-curvatures

In this paper, we study $$\Xi $$ -curvature and H-curvature of a special class of Finsler metrics called general $$(\alpha ,\beta )$$ -metrics. We prove that every general $$(\alpha ,\beta )$$ -metric of almost vanishing H-curvature is of almost vanishing $$ \Xi $$ -curvature under certain conditions. Moreover, we study such Finsler metric with vanishing $$\Xi $$ -curvature and its interaction to the flag curvature.