In this paper we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we study a new non-Riemannian quantity defined by the S-curvature. We show some relationships among the flag curvature, the S-curvature, and the new non-Riemannian quantity.

In this paper, we study locally projectively flat fourth root Finsler metrics and their generalized metrics. We prove that if they are irreducible, then they must be locally Minkowskian.