Homogeneous Einstein (α, β)-metrics on compact simple Lie groups and spheres. (January 2017) - Yan, Zaili; Deng, Shaoqiang
Abstract: In this paper, we study homogeneous Einstein ( α, β ) -metrics on compact Lie groups and spheres. We first show that any left invariant Einstein ( α, β ) -metric on a connected compact simple Lie groups except SU ( 2 ) with vanishing S-curvature must be a Randers metric. Secondly, we prove that any Sp ( n + 1 ) -invariant Einstein ( α, β ) -metric on S 4 n + 3 ( n ∈ N + ) with vanishing S-curvature is either a Randers metric, or SU ( 2 n + 2 ) -invariant. Finally, we give a complete description of SU ( n + 1 ) -invariant Einstein Finsler metrics on S 2 n + 1 ( n ≥ 2 ) .