A Finsler metric F is said to be spherically symmetric if the orthogonal group O(n) acts as isometries of F. In this paper, we show that every spherically symmetric Finsler metric of isotropic Berwald curvature is a Randers metric. We also construct explicitly a lot of new isotropic Berwald spherically symmetric Finsler metrics.

We give a lot of new Finsler metrics of quadratic Weyl curvature which are non-trivial in the sense that these metrics are not of Weyl type. We also manufacture new Weyl metrics.