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

TL;DR

This paper investigates $ ext{ extsterling}$-$ ext{ exteta}$-Ricci solitons on weak Kenmotsu $f$-manifolds, exploring their properties and introducing new characteristics of $ ext{ exteta}$-Einstein metrics within this geometric framework.

Contribution

It adapts the $ ext{ extsterling}$-Ricci tensor to weak metric $f$-manifolds and studies the interaction of $ ext{ extsterling}$-$ ext{ exteta}$-Ricci solitons with weak $eta f$-Kenmotsu structures, revealing new features of $ ext{ exteta}$-Einstein metrics.

Findings

Interaction of $ ext{ extsterling}$-$ ext{ exteta}$-Ricci solitons with weak $eta f$-Kenmotsu structures analyzed.

New characteristics of $ ext{ exteta}$-Einstein metrics established.

Adaptation of $ ext{ extsterling}$-Ricci tensor to weak metric $f$-manifolds.

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.