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Zbl 1043.53036
Chaki, M. C.; Ghosh, M. L.
On quasi Einstein manifolds. (English)
[J] Indian J. Math. 42, No. 2, 211-220 (2000). ISSN 0019-5324

Summary: Quasi Einstein manifolds $(QE)_m$ $(n\ge 3)$ are studied. It is shown that the curvature tensor $'R$ of type $(0,4)$ of such a manifold can be expressed in terms of a symmetric tensor $B$ of type $(0,2)$ when $n=3$, but it cannot, in general, be thus expressed when $n>3$. It is further shown that when $n>3$, $R$ posesses the same property if the manifold is conformally flat.

MSC 2000:: *53C25 Special Riemannian manifolds

Keywords: symmetric tensor; conformally flat

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Zentralblatt MATH Berlin [Germany]