New Einstein–Randers metrics on some homogeneous manifolds

Abstract

Abstract In this article, we find several new non‐Riemannian Einstein–Randers metrics on some homogeneous manifolds arising from the exceptional Lie groups. Based on the discussions about generalized flag manifolds with second Betti number , we firstly prove that there exists Riemannian Einstein metrics on these homogeneous manifolds. Then, we prove that there exists non‐Riemannian Einstein–Randers metrics on these homogeneous manifolds.