Non-naturally reductive Einstein metrics on Sp(n)

摘要

We prove that Sp(2k + l) admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k) × Sp(k) × Sp(l))-invariant if k < l. It implies that every compact simple Lie group Sp(n) for n ≥ 4 admits at least 2[(n— 1)/3] non-naturally reductive left-invariant Einstein metrics.