Resumen de Positive Quaternionic Kähler manifolds and symmetry rank: II

Fuquan Fang

• Let $M$ be a positive quaternionic K\"ahler manifold of dimension $4m$. If the isometry group $\text{Isom}(M)$ has rank at least $\frac {m}2 +3$, then $M$ is isometric to $\Bbb HP^m$ or $Gr_2(\Bbb C^{m+2})$. The lower bound for the rank is optimal if $m$ is even.