Positive Quaternionic Kähler manifolds and symmetry rank: II

Let $M$ be a positive quaternionic Kähler 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.

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Published 1 January 2008