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Zbl 1076.53509
De, U.C.; Ghosh, Gopal Chandra
On generalized quasi Einstein manifolds. (English)
[J] Kyungpook Math. J. 44, No. 4, 607-615 (2004). ISSN 1225-6951

The authors define a generalized quasi Einstein manifold to be a Riemannian manifold $(M,g)$ for which the Ricci tensor~$S$ is of the form $$S(X,Y)=a\,g(X,Y) +b\,A(X)A(Y)+c\,B(X)B(Y)$$ where $a$, $b$ and $c$ are real numbers and $A$ and~$B$ are the dual one-forms to two orthogonal unit vector fields. This class of spaces generalizes Einstein manifolds ($b=c=0$) and quasi Einstein manifold ($c=0$). The authors prove certain results concerning such manifolds.
[Eric Boeckx (Leuven)]

MSC 2000:: *53C25 Special Riemannian manifolds

Keywords: generalized quasi Einstein manifold; generalized quasi-constant curvature

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