Generalized Ricci recurrent spacetimes (GR)_n are investigated in Gray's seven subspaces. It is proved that a (GR)_n spacetime in all subspaces but one is an Einstein spacetime. The subspace $ℐ$ cannot contain a (GR)_n spacetime. Further, the subspaces $ℐ\oplus \mathcal{A}$ and $ℐ\oplus \mathcal{B}$ reduce to $\mathcal{A}$ and $\mathcal{B}$, respectively. Next, we prove that a (GR)_n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field A^l is closed. Further, it is shown that the Ricci tensor of (GR)_n is Riemann compatible if A^l is closed. Finally, sufficient conditions are given on a (GR)_n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime.

在 Gray 的七个子空间中研究了广义 Ricci 循环时空 (GR) _{n 。}证明所有子空间中的一个(GR) _n时空只有一个是爱因斯坦时空。子空间$ℐ$不能包含 (GR) _n时空。此外，子空间$ℐ\oplus \mathcal{A}$和$ℐ\oplus \mathcal{乙}$减少到$\mathcal{A}$和$\mathcal{乙}$， 分别。接下来，我们证明 a (GR) _n时空是 Ricci 半对称当且仅当时空是爱因斯坦或矢量场A ^l是闭合的。此外，如果A ^l闭合，则表明 (GR) _{n的 Ricci 张量是黎曼相容的。最后，在 (GR) n}翘曲乘积流形上给出充分条件以保证因子流形是爱因斯坦。此外，证明广义 Ricci 循环 GRW 时空是爱因斯坦时空。