We give a one-parameter family of examples of shrinking Laplacian solitons, which are the second known solutions to the closed G2-Laplacian flow with a finite-time singularity. The torsion forms and the Laplacian and Ricci operators of a large family of G2-structures on different Lie groups are also studied. We apply these formulas to prove that, under a suitable extra condition, there is no closed eigenform for the Laplacian on such family.

中文翻译：

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收缩拉普拉斯孤子的新例子

我们给出了收缩拉普拉斯孤子的单参数系列示例，这是具有有限时间奇点的封闭 G2-拉普拉斯流的第二个已知解。还研究了不同李群上的一大类 G2 结构的扭转形式以及拉普拉斯算子和里奇算子。我们应用这些公式来证明，在适当的额外条件下，该族上的拉普拉斯算子不存在闭特征形。