Author
Yan Zhao
Bio: Yan Zhao is an academic researcher from Henan University of Technology. The author has contributed to research in topics: Lie group. The author has an hindex of 1, coauthored 1 publications receiving 12 citations.
Topics: Lie group
Papers
More filters
••
TL;DR: In this article, it was shown 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.
Abstract: Abstract Let (M, g) be a nonKenmotsu (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 3manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.
24 citations
Cited by
More filters
••
TL;DR: In this article, the Ricci soliton is shown to be Ricci flat and locally isometric with respect to the Euclidean distance of the potential vector field when the manifold satisfies gradient almost.
Abstract: In the present paper, we initiate the study of $$*$$

$$\eta $$
Ricci soliton within the framework of Kenmotsu manifolds as a characterization of Einstein metrics. Here we display that a Kenmotsu metric as a $$*$$

$$\eta $$
Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have developed the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost $$*$$

$$\eta $$
Ricci soliton. Next, we deliberate $$*$$

$$\eta $$
Ricci soliton admitting $$(\kappa ,\mu )^\prime $$
almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to $${\mathbb {H}}^{n+1}(4)\times {\mathbb {R}}^n$$
. Finally we present some examples to decorate the existence of $$*$$

$$\eta $$
Ricci soliton, gradient almost $$*$$

$$\eta $$
Ricci soliton on Kenmotsu manifold.
8 citations
••
TL;DR: In this article, it was shown that if the metric g represents a Yamabe soliton, then it is locally isometric to the product space and the contact transformation is a strict infinitesimal contact transformation.
Abstract: Let $$(M^{2n+1},\phi ,\xi ,\eta ,g)$$
be a nonKenmotsu almost Kenmotsu $$(k,\mu )'$$
manifold. If the metric g represents a Yamabe soliton, then either $$M^{2n+1}$$
is locally isometric to the product space $$\mathbb {H}^{n+1}(4)\times \mathbb {R}^n$$
or $$\eta $$
is a strict infinitesimal contact transformation. The later case can not occur if a Yamabe soliton is replaced by a gradient Yamabe soliton. Some corollaries of this theorem are given and an example illustrating this theorem is constructed.
6 citations
••
TL;DR: In this paper, the authors prove a nonexistence result for Ricci solitons on noncosymplectic manifolds, and prove the same result for almost cosympelous manifolds.
Abstract: In this short note, we prove a nonexistence result for $$*$$
Ricci solitons on noncosymplectic $$(\kappa ,\mu )$$
almost cosymplectic manifolds.
6 citations
••
15 Apr 2021
TL;DR: In this article, it was shown that Bach flat almost coKahler manifold admits Ricci solitons, satisfying the critical point equation (CPE) or Bach flat.
Abstract: In this paper, we study an almost coKahler manifold admitting certain metrics such as $$*$$
Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. First, we consider a coKahler 3manifold (M, g) admitting a $$*$$
Ricci soliton (g, X) and we show in this case that either M is locally flat or X is an infinitesimal contact transformation. Next, we study noncoKahler $$(\kappa ,\mu )$$
almost coKahler metrics as CPE metrics and prove that such a g cannot be a solution of CPE with nontrivial function f. Finally, we prove that a $$(\kappa , \mu )$$
almost coKahler manifold (M, g) is coKahler if either M admits a divergence free Cotton tensor or the metric g is Bach flat. In contrast to this, we show by a suitable example that there are Bach flat almost coKahler manifolds which are noncoKahler.
6 citations