On General $( alpha, beta)$-Metrics with Some Curvature Properties

Abstract

In this paper, we study a class of Finsler metric called general $(alpha, beta)$ metrics and obtain an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence of this result, we prove that a general $(alpha, beta)$-metric has almost vanishing $H$-curvature if and only if it has almost vanishing $Xi$-curvature.