A Note on Gradient $\ast$-Ricci Solitons

Year 2020, , 79 - 85, 15.10.2020

Krishnendu De

https://doi.org/10.36753/mathenot.727083

Abstract

In the offering exposition we characterize $(k,\mu)'$- almost Kenmotsu $3$-manifolds admitting gradient $\ast$-Ricci soliton. It is shown that a $(k,\mu)'$- almost Kenmotsu manifold with $k<-1$ is admitting a gradient $\ast$-Ricci soliton, either the soliton is steady or the manifold is locally isometric to a rigid gradient Ricci soliton $\mathbb{H}^{2}(-4)\times \mathbb{R}$.                                                                                                                                 .                                                                      

Keywords

$(k \mu)'$- almost Kenmotsu manifolds, $\ast$-Ricci solitons, gradient $\ast$-Ricci solitons

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