η-Ricci Solitons on Weak β-Kenmotsu f-Manifolds

Recent interest among geometers in f-structures of K. Yano is due to the study of topology and dynamics of contact foliations, which generalize the flow of the Reeb vector field on contact manifolds to higher dimensions. Weak metric structures introduced by the author and R. Wolak as a generalization of Hermitian and Kähler structures, as well as f-structures, allow for a fresh perspective on the classical theory. In this paper, we study a new f-structure of this kind, called the weak (Formula presented.) -Kenmotsu f-structure, as a generalization of K. Kenmotsu’s concept. We prove that a weak (Formula presented.) -Kenmotsu f-manifold is a locally twisted product of the Euclidean space and a weak Kähler manifold. Our main results show that such manifolds with (Formula presented.) and equipped with an (Formula presented.) -Ricci soliton structure whose potential vector field satisfies certain conditions are (Formula presented.) -Einstein manifolds of constant scalar curvature.