Homogeneous Einstein-Randers metrics on some Stiefel manifolds

Stiefel manifolds VqRn of all orthonormal q-frames in Rn are diffeomorphic to the homogeneous space SO(n)∕SO(n−q). In this paper, we prove that there exist at least four homogeneous Einstein-Randers metrics on SO(n)∕SO(n−4)(n≥6), Moreover, we get at least six homogeneous Einstein-Randers metrics on SO(7)∕SO(2).