论文标题
具有离散各向同性的均质空间的仿射转化组
The group of affine transformations of homogeneous spaces with discrete isotropy
论文作者
论文摘要
我们提出了一种在特定条件下计算均质$ g $空间的仿射转换组的方法：当组$ g $和均质$ g $ -s-space允许线性连接时，自然投影是仿射的，并且具有离散的同位素组。如果$ g $承认双向线性连接，我们建立了均匀空间承认不变的线性连接的条件。结果，当各向同性组离散时，它们各自的仿射转化组是局部同构的。作为我们工作的应用，我们计算了可定向平坦仿射表面和3维平坦仿射Tori的仿射转化组。
We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and with discrete isotropy group. If $G$ admits a bi-invariant linear connection, we establish conditions under which the homogeneous space admits an invariant linear connection. As a consequence, when the isotropy group is discrete, their respective groups of affine transformations are locally isomorphic. As an application of our work, we calculate the group of the affine transformations of orientable flat affine surfaces and 3-dimensional flat affine tori.
