2016/03/16 by B. B. Chaturvedi, Pankaj Pandey, Chaturvedi, B. B. +1
Mathematics · Physics and Astronomy · #53C25 #53C55 #53C80 #Advanced Differential Geometry Research #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1603.05043
openalex publication_date 2016/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.