Finsler warped product metrics of quadratic Weyl curvature

The Weyl curvature is one of the most fundamental quantities in projective Finsler geometry. In this paper, we study a class of Finsler warped product metrics with quadratic Weyl curvature. We give necessary and sufficient conditions of such metrics to be of quadratic Weyl curvature which are non-trivial in the sense that these metrics are not of Weyl type, refining a theorem due to Gabrani-Sevim-Shen. As its application, we construct infinitely many new non-trivial W-quadratic Finsler warped product metrics. In particular, we find non-trivial W-quadratic Finsler metrics which are not Douglas type.