*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

Abstract

Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

∗-Ricci Tensor onα-Cosymplectic Manifolds

“…Recently, the study of * -Ricci solitons within the context of almost contact and paracontact manifolds were carried out in the studies [18,[29][30][31][32][33][34] and drawn several interesting results. In this section, we intended to * -Ricci soliton on a α-cosymplectic manifold.…”

η-∗-Ricci Solitons and Almost co-Kähler Manifolds

“…In a recent paper Wang [23] studied Ricci solitons and gradient Ricci solitons in (k, µ)ackms. In recent years, some researchers have also studied * -Ricci solitons in the frame work of contact and paracontact manifolds [21,[24][25][26]. To our knowledge, there are no results in the literature regarding * -Ricci solitons in ackms or (k, µ)-ackms in particular, nor in perfect fluid spacetimes.…”

Geometry of almost contact metrics as almost $*$-Ricci solitons

“…Recently, Ghosh-Patra [14] studied * -Ricci soliton and gradient almost * -Ricci soliton on contact metric manifolds. Later on, several mathematician studied * -Ricci soliton on contact and almost contact metric manifolds (e.g., see [6,7,28,29]). Furthermore, Venkatesh et al [28] proved that if an η-Einstein Kenmotsu manifold admits a * -Ricci soliton, then it is Einstein.…”