## On conformally flat special quasi Einstein manifolds.(English)Zbl 1075.53039

A quasi-Einstein manifold is a Riemannian manifold $$(M,g)$$ whose Ricci tensor $$S$$ is given by $$S=ag+bA\otimes A$$ for some $$C^\infty$$ functions $$a$$, $$b$$ and some 1-form $$A$$. The authors derive some tensor identities on a quasi Einstein manifold $$M$$ under the additional condition that $$(M,g)$$ is conformaly flat. From the results: if $$(M,g)$$ is a $$n$$-dimensional $$(n\geq 4)$$ conformally flat quasi-Einstein manifold with $$a \in \mathbb R$$, then $$(M,g)$$ is $$s$$ space of quasi-constant curvature.

### MSC:

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