Ricci Solitons in β-Kenmotsu Manifolds

The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.