# zbMATH — the first resource for mathematics

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.)