Finsler metrics with special Riemannian curvature properties

Abstract

Available online xxxx Communicated by Z. Shen MSC: 53B40 53C60 Keywords: Finsler metric Weyl curvature Riemann curvature W -quadraticThe Weyl curvature is one of the fundamental quantities in Finsler geometry because it is a projective invariant. By determining the Weyl curvature of a class of Finsler metrics, we find a lot of Finsler metrics of quadratic Weyl curvature which are non-trivial in the sense that they are not of quadratic Riemann curvature.