Invariant fourth root Finsler metrics on the Grassmannian manifolds

Fourth root metrics are a special and important class of Finsler metrics, which have been applied to physics. In this paper, we study invariant fourth root Finsler metrics on the Grassmannian manifolds SO(p+q)/SO(p)×SO(q)SO(p+q)/SO(p)×SO(q). By using the results from the theory of invariant polynomials of Lie groups, we obtain a complete classification of such metrics. Further, some invariant 2m2m-th root Finsler metrics are also given.