Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold - Ghosh, A. (Carpathian Mathematical Publications, 2019)
First, we prove that if the Reeb vector field ξ of a Kenmotsu manifold M leaves the Ricci operator Q invariant, then M is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) V is a contact vector field, or (ii) the Reeb vector field ξ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is η-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.