Curvature inheritance symmetry on M-projectively flat spacetimes

Abstract

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 [Formula: see text], when spacetime admits the conditions of both CI symmetry and conformal motion or motion along the vector field [Formula: see text]. 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 [Formula: see text]. 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 [Formula: see text] 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.