Invariant Einstein–Randers metrics on Stiefel manifolds

Abstract

A Finsler manifold (M,F) is called Einstein if its Ricci scalar does not depend on the flagpole. We obtain new examples of homogenous Einstein–Randers metrics on some Stiefel manifolds SO(n)/SO(l), as well as the symplectic analogs Sp(n)/Sp(l). An existence result of invariant Einstein–Randers metrics is also obtained on these homogeneous manifolds. We also give a classification of these metrics under isometries and determine their group of isometries.