## On quasi Einstein manifolds.(English)Zbl 0968.53030

The authors define a quasi Einstein manifold to be a non-flat Riemannian manifold $$(M^n,g)$$, $$n>2$$, such that its Ricci tensor $$S$$ satisfies the condition $$S(X,Y)=a g(X,Y) + b A(X) A(Y),$$ where $$a,b\neq 0$$ are associated scalars and $$A$$ is a non-zero associated 1-form such that $$g(X,U)=A(X)$$, $$g(U,U)=1$$. The associated scalars and 1-form are used to describe some properties of quasi Einstein manifolds. Namely conditions for $$M$$ to be conformally conservative are described.

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)