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arXiv · 2506.08973

$\ast$-$\eta$-Ricci solitons on weak Kenmotsu $f$-manifolds

Vladimir Rovenski
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Abstract

Recent interest among geometers in $f$-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric $f$-structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as $f$-structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak $\beta f$-Kenmotsu manifold defined as a generalization of K. Kenmotsu's concept. In this paper, the concept of the $\ast$-Ricci tensor of S. Tashibana is adapted to weak metric $f$-manifolds, the interaction of $\ast$-$\eta$-Ricci soliton with the weak $\beta f$-Kenmotsu structure is studied and new characteristics of $\eta$-Einstein metrics are obtained.

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Vladimir Rovenski. 2025-06-10. $\ast$-$\eta$-Ricci solitons on weak Kenmotsu $f$-manifolds. https://arxiv.org/abs/2506.08973

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