In this paper, we give some characterizations by considering almost ∗-$\eta$-Ricci–Bourguignon soliton as a Kenmotsu metric. It is shown that if a Kenmotsu metric endows a ∗-$\eta$-Ricci–Bourguignon soliton, then the curvature tensor R with the soliton vector field V is given by the expression $({{ℒ}}_{V}R)(V_1,\xi )\xi =2𝜗\{V_1(r)\xi -V_1(Dr)+\xi (Dr)-\xi (r)\xi -Dr\}.$ Next, we show that if an almost Kenmotsu manifold such that $\xi$ belongs to ${(\kappa ,-2)}^{\prime }$-nullity distribution where $\kappa <-1$ acknowledges a ∗-$\eta$-Ricci–Bourguignon soliton satisfying $\mathrm{\Omega }+\psi \ne 𝜗[(r+4n^2)+\{\xi (\xi (r))-\xi (Dr)\}]$, then the manifold is Ricci-flat and is locally isometric to ${ℍ}^{n+1}(-4)\times {ℝ}^n$. Moreover if the metric admits a gradient almost ∗-$\eta$-Ricci–Bourguignon soliton and $\xi$ leaves the scalar curvature r invariant on a Kenmotsu manifold, then the manifold is an $\eta$-Einstein. Also, if a Kenmotsu metric represents an almost ∗-$\eta$-Ricci–Bourguignon soliton with potential vector field V is pointwise collinear with $\xi$, then the manifold is an $\eta$-Einstein.

在本文中，我们通过考虑几乎*-来给出一些特征$\eta$-作为 Kenmotsu 度量的 Ricci-Bourguignon 孤子。结果表明，如果 Kenmotsu 度量赋予 ∗-$\eta$-Ricci-Bourguignon 孤子，则曲率张量R与孤子矢量场V由以下表达式给出$（{{ℒ}}_V右）（V_1,\Psi ）\Psi =2𝜗\{V_1（r）\Psi -V_1（Dr）+\Psi （Dr）-\Psi （r）\Psi -Dr\}。$接下来，我们证明如果一个几乎 Kenmotsu 流形使得$\Psi$属于${（\kappa ,-2）}^{\prime }$-无效分布，其中$\kappa <-1$承认*-$\eta$- 里奇-布吉尼翁孤子满足$\mathrm{\Omega }+\psi \ne 𝜗[（r+4n^2）+\{\Psi （\Psi （r））-\Psi （Dr）\}]$，则流形是 Ricci 平坦的并且局部等距于${ℍ}^{n+1}（-4）\times {ℝ}^n$。此外，如果度量承认梯度几乎 ∗-$\eta$- 里奇-布吉尼翁孤子和$\Psi$使标量曲率r在 Kenmotsu 流形上不变，则流形是$\eta$-爱因斯坦。另外，如果 Kenmotsu 度量表示几乎 ∗-$\eta$-具有势矢量场V的 Ricci–Bourguignon 孤子与$\Psi$，那么流形是$\eta$-爱因斯坦。