Space-time admitting generalized conharmonic curvature tensor.

The object of the present paper is to study space-time admitting generalized conharmonic curvature tensor. In this paper, we have studied the basic algebraic properties of generalized conharmonic curvature tensor. Next, it is proved that a 4-dimensional relativistic generalized conharmonic flat space-time is an Einstein space-time and it is of constant curvature. Moreover, it is of O-type. It is also observed that in a 4-dimensional relativistic perfect fluid generalized conharmonically flat space-time following Einstein's field equation in the absence of cosmological constant, energy momentum tensor is covariant constant. Finally, it is proved that a 4-dimensional relativistic conservative generalized conharmonic space-time M with constant scalar function ψ is a GRWspace-time. [ABSTRACT FROM AUTHOR]