Non-geodesic Orbit Einstein–Randers Metrics on SO(n)

Abstract

In this article, we prove that every compact simple Lie group SO(3k+ 2) (k ≥ 6) admits at least two non-naturally reductive Ad(SO(k) × SO(k + 1) × SO(k + 1))-invariant Einstein metrics, and prove that there are at least two non-naturally reductive Einstein metrics on compact simple Lie group SO(8n) (n ≥ 26), which are Ad(SO(2n) × SO(3n) × SO(3n))-invariant. Besides, we prove that the two non-naturally reductive Ad(SO(k) × SO(k +1) × SO(k + 1))-invariant Einstein metrics are also non-geodesic orbit. Finally, we obtain two non-geodesic orbit Einstein–Randers metrics on SO(3k + 2) (k ≥ 6).

Keywords

Non-naturally reductive metric / Einstein Randers metric / non-geodesic orbit / 53C25 / 53C30

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