Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit (Q1704650)

In previous works, invariant Einstein metrics which are not naturally reductive were obtained on the compact simple Lie groups \({\mathrm{SO}}(n)\), \({\mathrm{SU}}(n)\), \({\mathrm{Sp}}(n)\), \({\mathrm{E}}_6\), \({\mathrm{E}}_7\), \({\mathrm{E}}_8\) and \({\mathrm{F}}_4\). In other works, invariant Einstein metrics which is not ``geodesic orbit'' was obtained on \({\mathrm{G}}_2\). On the present work, it is shown that the above-mentioned metrics which are not naturally reductive are neither ``geodesic orbit''. The techniques from the generalized Wallach spaces are used for the proof.