Abstract
( C S ) 4 -spacetimes with Einstein field equations under some curvature restriction named generalized weakly Ricci-symmetry have been studied. We have proved that if the characteristic vector field ξ of a generalized weakly Ricci-symmetric ( C S ) 4 -spacetime obeying Einstein equation is a Killing vector field, then such a spacetime admits (i) curvature collineation, (ii) conformal collineation, (iii) conharmonic collineation, (iv) concircular collineation, (v) projective collineation, (vi) m -projective collineation. It is further proved that each of conformally flat , conharmonically flat, concircularly flat, projectively flat and m -projectively flat generalized weakly Ricci-symmetric ( C S ) 4 -spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field ξ .
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