缩小拉普拉斯孤子的新例子

arXiv: Differential Geometry Pub Date : 2020-06-23 DOI:10.1093/qmath/haab029

Marina Nicolini

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引用次数: 11

摘要

我们给出了一类单参数的缩形拉普拉斯孤子的例子，它们是具有有限时间奇点的闭$G_2$-拉普拉斯流的第二已知解。研究了一类大族$G_2$-结构在不同李群上的扭转形式及拉普拉斯算子和里奇算子。我们应用这些公式证明了在适当的附加条件下，该类上的拉普拉斯算子不存在闭特征型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New Examples Of Shrinking Laplacian Solitons

We give a one-parameter family of examples of shrinking Laplacian solitons, which are the second known solutions to the closed $G_2$-Laplacian flow with a finite-time singularity. The torsion forms and the Laplacian and Ricci operators of a large family of $G_2$-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.

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arXiv: Differential Geometry

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