We provide the second-known example of an extremally Ricci pinched closed $G_2$-structure on a compact 7-manifold, by finding a lattice in the only unimodular solvable Lie group admitting a left-invariant $G_2$-structure. Furthermore, the Laplacian coflow and its solitons are studied on a 6-parameter family of left-invariant coclosed $G_2$-structures on this Lie group. In this way, we obtain a 4-parameter subfamily of expanding solitons. The family is locally pairwise non-equivalent.

中文翻译：

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紧凑型 ERP G2 结构的新示例

我们提供了第二个已知的极端 Ricci 捏合的例子$G_2$- 紧致 7 流形上的结构，通过在唯一的单模可解李群中找到一个格子，该李群承认一个左不变量$G_2$-结构体。此外，在左不变共闭的 6 参数族上研究了拉普拉斯协流及其孤子$G_2$-这个李群的结构。通过这种方式，我们得到了一个 4 参数的膨胀孤子亚族。该族是局部成对非等价的。