Impact of symmetry inheritance on conformally flat spacetime

The goal of this research paper is to investigate curvature inheritancesymmetry in conformally flat spacetime. Curvature inheritance symmetry inconformally flat spacetime is shown to be a conformal motion. We have proventhat a conformally flat spacetime reduces to Einstein spacetime if admits curvature inheritance symmetry. A few results on conformally flat spacetimesthat obey Einstein’s field equation with or without a cosmological constant,if admits the curvature inheritance symmetry. The energy-momentum tensor is to be covariantly constant in a 4-dimensional relativistic perfect fluidspacetime which is also conformally flat spacetime, admits curvature inheritance, and obeys Einstein’s field equations in the presence of a cosmologicalconstant