  In this paper, the theory of space-time in 4-dimensional Kaehler manifold has
been studied. We have discussed the Einstein equation with cosmological
constant in perfect fluid Kaehler space-time manifold and proved that the
isotropic pressure, energy density and the energy momentum tensor vanish and
such a space-time manifold is an Einstein manifold. We have shown also that a
conformally flat perfect fluid Kaehler space-time manifold is infinitesimally
spatially isotropic relative to the velocity vector field. In last two
sections, we have studied weakly symmetric and weakly Ricci symmetric perfect
fluid Kaehler space-time manifolds and it has been shown, either the manifold
is of zero scalar curvature or the associated vector fields rho and alpha are
related by g(rho,alpha) = 4. At last, we have proved that the weakly Ricci
symmetric perfect fluid Kaehler space-time manifold of non-zero scalar
curvature does not exist.
