-Ricci solitons and gradient almost -Ricci solitons on Kenmotsu manifolds
In this paper, we consider -Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold is a -Ricci soliton, then soliton constant is zero. For 3-dimensional case, if admits a -Ricci soliton, then we show that is of constant sectional curvature -1. Next, we show that if admits a -Ricci soliton whose potential vector field is collinear with the characteristic vector field , then is Einstein and soliton vector field is equal to . Finally, we prove that if is a gradient almost -Ricci soliton, then either is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of . We verify our result by constructing examples for both -Ricci soliton and gradient almost -Ricci soliton.