Invariant Einstein metrics on Ledger-Obata spaces

In this paper, we study invariant Einstein metrics on Ledger-Obata spaces $F^m\mathrm{/}\mathrm{diag}(F)$. In particular, we classify invariant Einstein metrics on $F^4\mathrm{/}\mathrm{diag}(F)$ and estimate the number of invariant Einstein metrics on general Ledger-Obata spaces $F^m\mathrm{/}\mathrm{diag}(F)$.