Non-naturally reductive Einstein metrics on $\mathrm{SO}(n)$

Huibin Chen, Zhiqi Chen, Shaoqiang Deng

In this article, we prove that every compact simple Lie group $SO(n)$ for $n\ge 10$ admits at least $2\left([\frac{n-1}{3}]-2\right)$ non-naturally reductive left-invariant Einste…