×

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.)
PDF BibTeX XML Cite