LETTERS IN MATHEMATICAL PHYSICS, vol.112, no.2, 2022 (SCI-Expanded)
In the first part of the article, the definition of pseudo-symmetric spacetime is given. In the second part, the conditions under which a four-dimensional pseudo-symmetric spacetime has Riemann compatible and Weyl compatible vector fields are obtained, and the spacetime is examined considering the case that this spacetime is a generalized Robertson-Walker spacetime. In the third part of the article, some investigations on four-dimensional pseudo-symmetric spacetimes admitting F(R)-gravity are made.