Homogeneous Einstein–Randers metrics on symplectic groups

Abstract

In this paper, we prove that Lie group Sp(n)(n≥3) admits at least one family of invariant Einstein–Randers metrics, which are not naturally reductive. We also give the classification of these metrics under isometries and determine their group of isometries. Moreover, we prove that if homogeneous Randers space (M,F) with navigation data (h,W) is Berwald, then (M,F) is naturally reductive if and only if the Riemannian metric (M,h) is naturally reductive.