Geometric Characterizations of Almost Ricci-Bourguignon Solitons on Kenmotsu Manifolds

Abstract

The aim of this paper is to find the geometric characterizations of almost Ricci-Bourguignon solitons and gradient almost Ricci-Bourguignon solitons within the background of Kenmotsu manifolds. If $(M, g)$ is a (2n+1)-dimensionaal Kenmotsu manifold and $g$ represents an almost Ricci-Bourguignon soliton, then we find a sufficient condition under which the manifold $M$ is Einstein (trivial). Next, we show that if $g$ is an almost Ricci-Bourguignon soliton on $M$ and the Reeb vector field $\xi$ leaves $\lambda +\rho r$ invariant, then $g$ reduces to Ricci-Bourguignon soliton on $M$. Finally, we prove that if $g$ is a gradient almost Ricci-Bourguignon soliton, then the manifold $M$ is either Einstein or $g$ is a gradient $\eta-$Yamabe soliton on $M$. As a consequence of the results, we obtain several corollaries.