Let $(M^{2n+1},phi,xi,eta,g)$ be a $(k,mu)'$-almost Kenmotsu manifold with $k<-1$ which admits a gradient Ricci almost soliton $(g,f,lambda)$, where $lambda$ is the soliton function and $f$ is the potential function. In this paper, it is proved that $lambda$ is a constant and this implies that $M^{2n+1}$ is locally isometric to a rigid gradient Ricci soliton $mathbb{H}^{n+1}(-4)imesmathbb{R}^n$, and the soliton is expanding with $lambda=-4n$. Moreover, if a three dimensional Kenmotsu manifold admits a gradient Ricci almost soliton, then either it is of constant sectional curvature $-1$ or the potential vector field is pointwise colinear with the Reeb vector field.
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机译：令$ {M ^ {2n + 1}， phi， xi， eta，g）$为$（k， mu）'$-几乎Kenmotsu流形，其中$ k <-1 $允许梯度Ricci几乎孤子$（g，f， lambda）$，其中$ lambda $是孤子函数，而$ f $是势函数。本文证明$ lambda $是一个常数，这意味着$ M ^ {2n + 1} $与刚性梯度Ricci孤子$ mathbb {H} ^ {n + 1}（ -4） times mathbb {R} ^ n $，孤子以$ lambda = -4n $扩展。此外，如果三维Kenmotsu流形允许近似Ricci的梯度孤子，那么它要么具有恒定的截面曲率$ -1 $，要么势矢量场与Reeb矢量场成点共线。
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