Almost $\eta$-Ricci solitons in $(LCS)_n$-manifolds

TL;DR

This paper investigates almost $\eta$-Ricci solitons within $(LCS)_n$-manifolds, establishing bounds on Ricci curvature and deriving formulas that deepen understanding of their geometric properties.

Contribution

It introduces new bounds and formulas for almost $\eta$-Ricci solitons in $(LCS)_n$-manifolds under specific curvature conditions.

Findings

Bounds for Ricci curvature in gradient cases

A Bochner-type formula for almost $\eta$-Ricci solitons

Consequences of the formula on $(LCS)_n$-manifolds

Abstract

We consider almost $\eta$-Ricci solitons in $(LCS)_n$-manifolds satisfying certain curvature conditions. We provide a lower and an upper bound for the norm of the Ricci curvature in the gradient case, derive a Bochner-type formula for an almost $\eta$-Ricci soliton and state some consequences of it on an $(LCS)_n$-manifold.