Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, (GR)n structure are completely classified in this short report. A conformally flat generalized Ricci recurrent pseudo-Riemannian manifold is shown to be an Einstein manifold. In particular, a conformally flat generalized Ricci recurrent spacetime must be either a de Sitter spacetime or an anti-de Sitter spacetime.

中文翻译：

---

共形平坦广义 Ricci 递归伪黎曼流形的分类

具有广义 Ricci 循环的共形平坦伪黎曼流形，(GR)n结构在这份简短的报告中完全分类。一个共形平坦的广义 Ricci 递归伪黎曼流形被证明是一个爱因斯坦流形。特别是，一个共形平坦的广义 Ricci 循环时空必须是德西特时空或反德西特时空。