Comprehensive quasi-Einstein spacetime with application to general relativity

The aim of this paper is to extend the notion all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed manifold, pseudo manifold and many more name it comprehensive quasi Einstein C(QE)$_{n}$. We investigate some geometric physical properties C(QE)$_{n}$ under certain conditions. study conformal conharmonic mappings between manifolds. Then we examine with harmonic Weyl tensor. define quasi-constant curvature proved that conformally flat vice versa. general two viscous fluid spacetime C(QE)$_{4}$ find out important consequences about C(QE)$_{4}$. vanishing space matter Finally, prove existence such by constructing non-trivial example.