Spacetimes admitting quasi-conformal curvature tensor

The object of the present paper is to study spacetimes admittingý ýquasi-conformal curvature tensorý. ýAt first we prove that a quasi-conformally flat spacetime is Einsteiný ýand hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfyingý ýEinstein's field equation with cosmological constant is covariant constantý. ýNextý, ýwe prove that if the perfect fluid pacetime withý ývanishing quasi-conformal curvature tensor obeys Einstein's field equation without cosmological constantý, ýthen the spacetime has constant energy density and isotropic pressure and the perfect fluid always behaveý ýas a cosmological constant and also such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field Uý. ýMoreoverý, ýit is shown that in a purely electromagnetic distribution the spacetime with vanishing quasi-conformal curvature tensor is filled withý ýradiation and extremely hot gasesý. ýWe also study dust-like fluid spacetime with vanishing quasi-conformal curvature tensor.