A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields

Abstract It is well-known that Einstein manifolds play an important role in geometry as well as in general relativity. Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds. The object of the present paper is to study some geometric properties of mixed-generalized quasi-Einstein Manifolds (MG(QE)n) which admitting certain vector fields. We show the existence of MG(QE)n, by constructing several non-trivial examples. Finally we study warped product on MG(QE)n and show that M = I×M∗ (dimI = 1 and dimM∗ = n − 1) is a MG(QE)n if M∗ is a generalized quasi-Einstein Manifold (G(QE)n).