Let $M$ be a quaternionic manifold, $\dim M=4k$, whose twistor space is aFano manifold. We prove the following: (a) $M$ admits a reduction to $Sp(1)\times GL(k,H)$ if and only if $M=HP^k$, (b) either $b_2(M)=0$ or$M=Gr_2(k+2,C)$. This generalizes results of S. Salamon and C.R. LeBrun,respectively, who obtained the same conclusions under the assumption that $M$is a complete quaternionic-Kaehler manifold with positive scalar curvature.
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机译：假设$ M $是四元数流形，$ \ dim M = 4k $，其扭曲空间为Fano流形。我们证明以下内容：（a）$ M $承认当且仅当$ M = HP ^ k $时，才可减少$ Sp（1）\ times GL（k，H）$，（b）$ b_2（M） = 0 $或$ M = Gr_2（k + 2，C）$。这分别概括了S.Salamon和C.R.LeBrun的结果，他们在$ M $是标量曲率为正的完整四元离子-Kaehler流形的假设下获得了相同的结论。
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