Abstract
In this paper, we deal with spacetimes allowing a semi-symmetric connection whose metric tensor is recurrent. We investigate the impact of this connection on spacetimes and establish a nontrivial example. We physically explain the properties of spacetime that we obtained. Under a certain condition, we demostrate that a spacetime admitting such a connection becomes the GRW spacetime as well as the anti-de Sitter and represents the dark matter era. Finally, we scrutinize in case such a spacetime admits a Ricci soliton and generalized Ricci soliton.
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