Homogeneous almost quaternion-Hermitian manifolds (Q383580)

The main results of the paper is the following classification: A compact simply connected homogeneous manifold \(M=G\slash H\) of non-vanishing Euler characteristic carries a homogeneous almost quaternion-Hermitian structure if and only if it belongs to the following list: {\parindent=0.5cm\begin{itemize}\item[--] Wolf spaces \(G\slash N\) where \(G\) is any compact simple Lie group and \(N\) is the normalizer of some subgroup \(\mathrm{Sp}(1)\subset G\) determined by a highest root of \(G.\) \item[--] \(\mathbb S^2\times\mathbb S^2.\) \item[--]\(\mathrm{SO}(7)/\mathrm{U}(3).\) \end{itemize}}