论文标题
$ g_2 $ - 平面索尔夫曼福尔德的结构
$G_2$-structures on flat solvmanifolds
论文作者
论文摘要
在本文中，我们研究了Flat Solvmanifolds和$ G_2 $ - 几何的关系。首先，我们使用$ \ Mathsf {gl}（n，\ Mathbb {Z}）$的有限亚组的分类对7维平面分解的solvmanifolds进行分类。然后，我们寻找封闭，共凝结和无差异的$ G_2 $ - 结构与平面度量兼容。特别是，我们提供了带有无扭转的$ g_2 $结构的紧凑型扁平流形的明确示例，其有限的自律是循环的，并包含在$ g_2 $中，以及紧凑的平面歧管的示例，承认不含差异的$ G_2 $结构。
In this article we study the relation between flat solvmanifolds and $G_2$-geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of $\mathsf{GL}(n,\mathbb{Z})$ for $n=5$ and $n=6$. Then, we look for closed, coclosed and divergence-free $G_2$-structures compatible with the flat metric on them. In particular, we provide explicit examples of compact flat manifolds with a torsion-free $G_2$-structure whose finite holonomy is cyclic and contained in $G_2$, and examples of compact flat manifolds admitting a divergence-free $G_2$-structure.
