Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42620161218Spacetimes admitting quasi-conformal curvature tensor15351546908ENS.MallickDepartment of Mathematics, Chakdaha College, P. O. Chakdaha,
Dist-Nadia, West Bengal, India.P.ZhaoDepartment of Applied Mathematics, Nanjing University of Science and Technology,
Nanjing 210094, P. R. China.U. C.DeDepartment of Pure Mathematics, University of Calcutta, 35, B. C. Road,
Kolkata 700019, West Bengal, India.Journal Article20150616The object of the present paper is to study spacetimes admitting quasi-conformal curvature tensor. At first we prove that a quasi-conformally flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein's field equation with cosmological constant is covariant constant. Next, we prove that if the perfect fluid pacetime with vanishing quasi-conformal curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has constant energy density and isotropic pressure and the perfect fluid always behave as a cosmological constant and also such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field $U$. Moreover, it is shown that in a purely electromagnetic distribution the spacetime with vanishing quasi-conformal curvature tensor is filled with radiation and extremely hot gases. We also study dust-like fluid spacetime with vanishing quasi-conformal curvature tensor. http://bims.iranjournals.ir/article_908_ca47683e2d4c028ece8b6d5e9a07b102.pdf