The subject of the present paper is the investigation of a new type of solitons, called $\eta$-∗-Ricci solitons in $(k,\mu )$-almost co-Kähler manifold (briefly, $ackm$), which generalizes the notion of the $\eta$-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on $ackm$ is obtained. Additionally, we classify the $\eta$-∗-Ricci solitons in $(k,\mu )$-$ackm$s. Next, we investigate $(k,\mu )$-$ackm$s admitting gradient $\eta$-∗-Ricci solitons. Finally, we construct two examples to illustrate our results.

In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h-almost Ricci–Yamabe solitons and h-almost gradient Ricci–Yamabe solitons, respectively. Finally, we construct an example to illustrate our result.

In this paper, we study ?-Ricci solitons on N(k)-contact metric manifolds. At first we consider ?-Ricci solitons on N(k)-contact metric manifolds with harmonic curvature tensor. Then we study ?-Ricci solitons onN(k)-contact metric manifolds with harmonic Weyl tensor. Moreover, we consider ?-Ricci soliton on N(k)-contact metric manifolds with ?-parallel Ricci tensor. Also ?-Ricci soliton on N(k)-contact metric manifolds satisfying some curvature restrictions under projective curvature tensor have been considered. Finally, the existence of an ?-Ricci soliton on a 3-dimensional N(k)-contact metric manifold is ensured by a proper example.