We investigate an obstruction for hypersymplectic manifolds equipped with a free, isometric action of SU$(1,1)$. When the obstruction vanishes, we show that the manifold is a metric cone over a split 3-Sasakian manifold. Furthermore, if the action of SU$(1,1)$ is also proper, then the hypersymplectic manifold fibres over a para-quaternionic Kähler manifold. We conclude the article with some examples for which the obstruction vanishes. In particular, we show that the moduli space to Nahm–Schmid equations admits a fibration over a para-quaternionic Kähler manifold.

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超辛流形和相关几何

我们调查了带有SU $（1,1）$自由，等距作用的高辛歧管的阻塞。当障碍物消失时，我们表明歧管是在分裂的3 Sasakian歧管上的公制圆锥。此外，如果SU $（1,1）$的作用也适当，则超四面体歧管纤维在准四元离子Kähler流形上。我们以一些阻碍消失的例子来结束本文。特别是，我们证明了Nahm–Schmid方程的模空间允许准四元离子Kähler流形上的纤维化。