Abstract
The object of the present paper is to study some classes of N(k)-quasi Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is killing as well as parallel unit vector fields under certain curvaturerestrictions.
Highlights
Let R denotes the Riemannian curvature tensor of a Riemannian manifold Mn
Let (Mn, g) be an n−dimensional N (k)-quasi Einstein manifold, it is a space of quasi constant curvature for each of curvature restriction and the condition
Let (Mn, g) be an n−dimensional N (k)−quasi Einstein manifold equipped with the cyclic parallel Ricci tensor satisfying R(ξ, X) · W ∗ = 0
Summary
Let R denotes the Riemannian curvature tensor of a Riemannian manifold Mn. For a smooth function k, the k−nullity distribution N (k) of a Riemannian manifold is defined as. The deviation conditions R(ξ, X)·R = 0, R(ξ, X)·S = 0 have been studied in [9], where R and S denote the curvature and Ricci tensors of the manifold respectively. The generalized quasi-conformal curvature tensor for n−dimensional manifold is defined as
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