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

Vladimir Rovenski ()
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Vladimir Rovenski: Department of Mathematics, University of Haifa, Haifa 3498838, Israel

Mathematics, 2025, vol. 13, issue 11, 1-15

Abstract: 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 β -Kenmotsu f -structure, as a generalization of K. Kenmotsu’s concept. We prove that a weak β -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 β = c o n s t and equipped with an η -Ricci soliton structure whose potential vector field satisfies certain conditions are η -Einstein manifolds of constant scalar curvature.

Keywords: twisted product; β -Kenmotsu f -manifold; η -Einstein manifold; η -Ricci soliton (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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