Our aim is to characterize the Lorentzian manifolds endowed with a type of semi-symmetric non-metric connection. It is proven that a Lorentzian manifold with a type of semi-symmetric non-metric connection is a GRW space-time. To minimize the gap between the RW space-time and the GRW space-time, we establish a bridge between them. It is shown that a weakly Ricci symmetric GRW space-time is a stiff matter fluid. We also classify the space-times by using the Petrov's classification. Finally, we construct an example of a 4-dimensional Lorentzian manifold admitting a semi-symmetric non-metric connection whose associated vector field is a unit timelike concircular vector field.

我们的目的是表征具有一种半对称非度量连接的洛伦兹流形。事实证明，具有半对称非度量连接类型的洛伦兹流形是GRW时空。为了使RW时空与GRW时空之间的差距最小，我们在它们之间建立了一座桥梁。结果表明，弱Ricci对称GRW时空是一种硬质流体。我们还使用彼得罗夫（Petrov）的分类对时空进行分类。最后，我们构造一个四维洛伦兹流形的一个例子，该流形接受一个半对称的非度量连接，其关联矢量场是单位时间似的圆形矢量场。