  As a generalization of Einstein manifolds, the nearly quasi-Einstein
manifolds and pseudo quasi-Einstein manifolds are both interesting and useful
in studying the general relativity. In this paper, we study the extended
quasi-Einstein manifolds which derive from pseudo quasi-Einstein manifolds.
After showing the existence theorem of extended quasi-Einstein manifold, we
give some special geometric properties of such manifolds. At the same time, we
also discuss the extended quasi-Einstein manifolds with certain soliton like
generalised Ricci soliton or Riemann soliton. Furthermore, we construct some
nontrivial example to illustrate these extended quasi-Einstein manifolds.
