We define the notion of affine Anosov representations of word hyperbolic groups into the affine group $\textsf {SO}^0(n+1,n)\ltimes {\mathbb {R}}^{2n+1}$. We then show that a representation $\rho $ of a word hyperbolic group is affine Anosov if and only if its linear part $\mathtt {L}_\rho $ is Anosov in $\textsf {SO}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic plane and $\rho (\Gamma )$ acts properly on $\mathbb {R}^{2n+1}$.

中文翻译：

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仿射 Anosov 表示和适当的操作

我们将单词双曲群的仿射 Anosov 表示定义为仿射群 $\textsf {SO}^0(n+1,n)\ltimes {\mathbb {R}}^{2n+1}$。然后我们证明一个词双曲群的表示 $\rho $ 是仿射 Anosov 当且仅当它的线性部分 $\mathtt {L}_\rho $ 是 $\textsf {SO}^0(n+1 ,n)$ 相对于最大各向同性平面的稳定器和 $\rho (\Gamma )$ 正确地作用于 $\mathbb {R}^{2n+1}$。