On a Lorentzian Complex Space Form

The aim of the present paper is to study the theory of general relativity in a Lorentzian Kahler space. In this paper, we have considered the Lorentzian complex space form with constant sectional curvature and proved that a Lorentzian complex space form satisfying Einstein's field equation is a Ricci semi-symmetric space and the energy-momentum tensor is covariant constant. Such space reduces to a flat space for a purely electromagnetic distribution. The existence of the Killing vector field and conformal Killing vector field has been discussed and proved that the cosmological term is proportional to sectional curvature. Further, it is shown that the perfect fluid in a Lorentzian complex space form satisfying Einstein's field equation does not admit heat flux.