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On generalized quasi Einstein manifolds. (English) Zbl 1076.53509
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.

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