A note on Ricci soliton in almost Kenmotsu manifold

TL;DR

This paper proves that Ricci solitons with the Reeb potential vector field cannot exist in almost Kenmotsu manifolds, clarifying a specific geometric property of these structures.

Contribution

It establishes a non-existence result for Ricci solitons with Reeb potential vector fields in almost Kenmotsu manifolds, a previously unexplored aspect.

Findings

Ricci solitons with Reeb potential vector field do not exist in almost Kenmotsu manifolds

The result clarifies geometric constraints of almost Kenmotsu manifolds

Provides insight into the structure of Ricci solitons in contact geometry

Abstract

In this short note it is established that there does not exist Ricci soliton with the Reeb potential vector field in an almost Kenmotsu manifold (briefly, $\mathcal{AKM}$).