Ricci Solitons in β -Kenmotsu Manifolds

Source abstract

Abstract 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 (ℒ Vg +2 S )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.