General (α, β)-metrics with constant Ricci and flag curvature

Abstract

General (α, β)-metrics form a rich and important class of Finsler metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a general (α, β) metrics. In this paper, we study the general (α, β)-metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general (α, β) metrics with vanishing χ-curvature.