The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with ★-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of ★-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.
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Yoldaş et al. (2023) studied this question.