We determine the spectrum of the sub-Laplacian on pseudo H -type nilmanifolds and present pairs of isospectral but non-homeomorphic nilmanifolds with respect to the sub-Laplacian. We observe that these pairs are also isospectral with respect to the Laplacian. More generally, our method allows us to construct an arbitrary number of isospectral but mutually non-homeomorphic nilmanifolds. Finally, we present two nilmanifolds of different dimensions such that the short time heat trace expansions of the corresponding sub-Laplace operators coincide up to a term which vanishes to infinite order as time tends to zero.

中文翻译：

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附加到 Clifford 模的一类 nilmanifolds 的谱理论

我们确定了伪 H 型 nilmanifolds 上的亚拉普拉斯算子的光谱，并提出了关于亚拉普拉斯算子的成对等谱但非同胚 nilmanifolds。我们观察到这些对对于拉普拉斯算子也是等谱的。更一般地，我们的方法允许我们构造任意数量的等谱但相互非同胚的nilmanifolds。最后，我们提出了两个不同维度的 nilmanifolds，使得相应的亚拉普拉斯算子的短时间热迹膨胀重合到一个随着时间趋于零而消失到无限阶的项。