The aim of this paper is to extend the notion of all known quasi-Einstein (QE) manifolds like generalized QE, mixed generalized QE manifold, pseudo generalized QE manifold and many more and name it comprehensive QE manifold $\mathrm{\text{Co(QE}}{)}_n$. We investigate some geometric and physical properties of the comprehensive QE manifolds $\mathrm{\text{Co(QE}}{)}_n$ under certain conditions. We study the conformal and conharmonic mappings between $\mathrm{\text{Co(QE}}{)}_n$ manifolds. Then we examine the $\mathrm{\text{Co(QE}}{)}_n$ with harmonic Weyl tensor. We define the manifold of comprehensive quasi-constant curvature and prove that conformally flat $\mathrm{\text{Co(QE}}{)}_n$ is manifold of comprehensive quasi-constant curvature and vice versa. We study the general two viscous fluid spacetime $\mathrm{\text{Co(QE}}{)}_4$ and find out some important consequences about $\mathrm{\text{Co(QE}}{)}_4$. We study $\mathrm{\text{Co(QE}}{)}_n$ with vanishing space matter tensor. Finally, we prove the existence of such manifolds by constructing nontrivial example.

本文的目的是扩展所有已知的准爱因斯坦 (QE) 流形的概念，如广义 QE、混合广义 QE 流形、伪广义 QE 流形等，并将其命名为综合 QE 流形 $\mathrm{\text{辅酶(QE}}{)}_n$. 我们研究了综合 QE 流形的一些几何和物理特性$\mathrm{\text{辅酶(QE}}{)}_n$在一定条件下。我们研究了之间的共形和共谐映射$\mathrm{\text{辅酶(QE}}{)}_n$流形。然后我们检查$\mathrm{\text{辅酶(QE}}{)}_n$与谐波 Weyl 张量。我们定义了综合准恒定曲率的流形并证明了共形平坦$\mathrm{\text{辅酶(QE}}{)}_n$是综合准恒定曲率的流形，反之亦然。我们研究一般的两个粘性流体时空$\mathrm{\text{辅酶(QE}}{)}_4$ 并找出一些重要的后果 $\mathrm{\text{辅酶(QE}}{)}_4$. 我们学习$\mathrm{\text{辅酶(QE}}{)}_n$与消失的空间物质张量。最后，我们通过构造非平凡的例子证明了这种流形的存在。