On generalized quasi Einstein manifolds. (English) Zbl 1076.53509

De, U. C.; Ghosh, Gopal Chandra

Kyungpook Math. J. 44, No. 4, 607-615 (2004).

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.

Reviewer: Eric Boeckx (Leuven)

MSC:

53C25

Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

generalized quasi Einstein manifold; generalized quasi-constant curvature