Ricci Solitons in β-Kenmotsu Manifolds

Abstract

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