Curvature inheritance symmetry on M-projectively flat spacetimes

The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M-projective curvature tensor follows the symmetry inheritance property along a vector field xi, when spacetime admits the conditions of both CI symmetry and conformal motion or motion along the vector field xi. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations (EFEs) with a cosmological term and admitting the CI symmetry along the vector field xi. We have shown that an M-projectively flat perfect fluid spacetime obeying the EFEs with a cosmological term and admitting the CI symmetry along a vector field xi is either a vacuum or satisfies the vacuum-like equation of state. We have also shown that such spacetimes with the energy-momentum tensor of an electromagnetic field distribution do not admit any curvature symmetry of general relativity. Finally, an example of M-projectively flat spacetime has been exhibited.