Homogeneous Einstein–Randers metrics on some Stiefel manifolds

Abstract

Stiefel manifolds V q R n of all orthonormal q -frames in R n 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 ) .