It is known that the almost-Kaehler anti-self-dual metrics on a given 4-manifold sweep out an open subset in the moduli space of anti-self-dual metrics. However, we show here by example that this subset is not generally closed, and so need not sweep out entire connected components in the moduli space. Our construction hinges on an unexpected link between harmonic functions on certain hyperbolic 3-manifolds and self-dual harmonic 2-forms on associated 4-manifolds.

中文翻译：

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反自双 $4$-流形、准 Fuchsian 群和几乎 Kähler 几何

众所周知，给定 4 流形上的几乎 Kaehler 反自对偶度量在反自对偶度量的模空间中扫出一个开放子集。然而，我们在这里通过例子表明，这个子集通常不是封闭的，因此不需要扫除模空间中的整个连通分量。我们的构造取决于某些双曲 3-流形上的调和函数与相关 4-流形上的自对偶调和 2-形式之间的意外联系。