On a non-Riemannian quantity of (α, β)-Metrics

Abstract

In this paper, we study a non-Riemannian quantity χ-curvature of (α, β)-metrics, a special class of Finsler metrics with Riemannian metric α and a 1-form β. We prove that every (α, β)-metric has a vanishing χ-curvature under certain conditions.