A Class of Finsler Metrics with Almost Vanishing H- and ?-curvatures

Abstract

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.