U. C. De | Searcharxiv

arXiv2024

$η$-Ricci Solitons on Kenmotsu 3-Manifolds

In the present paper we study $η$-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider $η$-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study $ϕ$-Ricci symmetric $η$-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition $R.R=Q(S,R)$ is considered. Finally, an example is constructed to prove the existence of a proper $η$-Ricci soliton on a Kenmotsu 3-manifold.

math.DG↗

arXiv2021

A note on Ricci soliton in almost Kenmotsu manifold

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, $\mathcal{AKM}$).

math.DG↗