# Ricci $\rho$-solitons on 3-dimensional $\eta$-Einstein almost Kenmotsu mandifolds

## TL;DR

This paper introduces Ricci ρ-solitons as a generalization of Ricci solitons inspired by Ricci-Bourguignon flow, and characterizes 3D almost Kenmotsu Einstein manifolds that admit such solitons.

## Contribution

It defines Ricci ρ-solitons in the context of almost Kenmotsu manifolds and proves their existence implies the manifold is a constant curvature Kenmotsu manifold.

## Key findings

- 3D almost Kenmotsu Einstein manifolds with Ricci ρ-solitons are of constant sectional curvature -1
- The Ricci ρ-soliton in this setting is expanding with λ=2
- The study links Ricci flow generalizations to specific geometric structures

## Abstract

In this paper the notion of Ricci $\rho$-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3- dimensional almost Kenmotsu Einstein manifold $M$ be a $\rho$-soliton, then $M$ is a Kenmotsu manifold of constant sectional curvature $-1$ and the $\rho$-soliton is expanding, with $\lambda =2$.