Ricci对李群上的$G_2$-结构进行了极值缩紧

Pub Date : 2019-02-18 DOI:10.4310/cag.2022.v30.n6.a5

J. Lauret, Marina Nicolini

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引用次数: 17

摘要

在文献中只能找到两个极端Ricci压缩的G2结构的例子，并且它们都是均匀的。本文研究了李群上这类特殊的闭G2结构的存在性和结构。证明了李代数上的强结构条件成立。作为一个应用，我们得到了三个极端Ricci压缩G2结构的新例子，它们都必然是稳定的拉普拉斯孤子。还对这种结构的变形和刚度进行了研究。

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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Extremally Ricci pinched $G_2$-structures on Lie groups

Only two examples of extremally Ricci pinched G2-structures can be found in the literature and they are both homogeneous. We study in this paper the existence and structure of such very special closed G2-structures on Lie groups. Strong structural conditions on the Lie algebra are proved to hold. As an application, we obtain three new examples of extremally Ricci pinched G2-structures and that they are all necessarily steady Laplacian solitons. The deformation and rigidity of such structures are also studied.

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