Curvature inheritance symmetry on M-projectively flat spacetimes

The paper aims to investigate curvature inheritance symmetry in M-projectively flat spacetimes. It is shown that the curvature inheritance 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 curvature inheritance 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 with a cosmological term and admitting the curvature inheritance symmetry along the vector field $\xi$. We have shown that an M-projectively flat perfect fluid spacetime obeying the Einstein field equations with a cosmological term and admitting the curvature inheritance 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.