A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields. Issue 2 (3rd July 2019) - Dey, Santu; Pal, Buddhadev; Bhattacharyya, Arindam
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 ).