Invariant Einstein metrics on certain homogeneous spaces (Q1365389)

The authors study existence and non-existence of homogeneous Einstein metrics on certain compact homogeneous spaces \(G/H\) whose isotropy representations decompose into three inequivalent irreducible summands and give examples of compact connected homogeneous spaces \(G/H\) that have \(G\)-invariant homogeneous Einstein metrics as well as examples which carry no \(G\)-invariant Einstein metrics.