A STUDY ON MANIFOLD KAEHLERIAIN SPACE

Abstract

This work delves into the space-time theory of the 4-dimensional Kaehler manifold. Since the isotropic pressure, energy density, and energy momentum tensor all vanish in a perfect fluid Kaehler space-time manifold, we have established that this space-time manifold is an Einstein manifold and studied the Einstein equation with a cosmological constant in it. Finally, we demonstrated that, on a conformally flat, perfectly fluid Kaehler space-time manifold, the velocity vector field is infinitesimally spatially isotropic. Ideal fluid dilution to the point where only Ricci and minimal symmetry hold. We have proven that Kaehler space-time manifolds have either 0 scalar curvature or a connection between the respective rho and alpha vector fields via g(rho,alpha) = 4. To conclude, we have proved that a Kaehler space-time manifold cannot have both perfect fluidity and non-zero scalar curvature (weak Ricci symmetry).