In this paper, we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtle sign terms in the G-spin theorem for an isometry, with isolated fixed points, of a closed spin hyperbolic 2- or 4-manifold.

中文翻译：

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戴维斯双曲 4 流形上的谐波旋量

在本文中，我们使用G-自旋定理表明戴维斯双曲 4 流形承认谐波旋量。这是闭合双曲线的第一个例子4-允许谐波旋量的流形。我们还明确描述了自旋双曲 2 或 4 流形的旋量丛，并展示了如何计算G-自旋定理，用于封闭自旋双曲线 2 或 4 流形的等距，具有孤立的固定点。