A Non-Flat Riemannian Manifold Admitting Certain Vectors Fields. Issue 2 (3rd July 2019)

• Record Type: Journal Article
• Authors: Dey, Santu; Pal, Buddhadev; Bhattacharyya, Arindam
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 17:Issue 2(2019)
• Page Start: 221
• Page End: 237
• Publication Date: 2019-07-03
• Subjects: 53C25 -- 53C15; Mixed-generalized quasi-Einstein manifolds -- Codazzi type of Ricci tensor -- cyclic parallel Ricci tensor -- Killing vector field -- concurrent vector field -- re- current vector field -- warped product manifold; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2019.1668148
• Languages: English
• ISSNs: 1726-037X

Abstract

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 ).