Yaning Wang

Bio: Yaning Wang is an academic researcher from Henan Normal University. The author has an hindex of 1, co-authored 1 publications receiving 2 citations.

Almost Kenmotsu $$(k,\mu )'$$ ( k , μ ) ′ -manifolds with Yamabe solitons

Abstract: Let $$(M^{2n+1},\phi ,\xi ,\eta ,g)$$ be a non-Kenmotsu 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.

Ricci-Yamabe solitons and 3-dimensional Riemannian manifolds

Abstract: : In this paper, we classify 3-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are Ricci-Yamabe solitons and gradient Ricci-Yamabe solitons, respectively. Finally, we construct an example to illustrate our result.

Yamabe and riemann solitons on lorentzian para-sasakian manifolds

Abstract: . In the present paper, we aim to study Yamabe soliton and Riemann soliton on Lorentzian para-Sasakian manifold. First, we proved, if the scalar curvature of an η -Einstein Lorentzian para-Sasakian manifold M is constant, then either τ = n ( n − 1) or, τ = n − 1. Also we constructed an example to justify this. Next, it is proved that, if a three dimensional Lorentzian para-Sasakian manifold admits a Yamabe soliton for V is an infinitesimal contact transformation and tr ϕ is constant, then the soliton is expanding. Also we proved that, suppose a 3-dimensional Lorentzian para-Sasakian manifold admits a Yamabe soliton, if tr ϕ is constant and scalar curvature τ is harmonic (i.e., ∆ τ = 0), then the soliton constant λ is always greater than zero with either τ = 2, or τ = 6, or λ = 6. Finally, we proved that, if an η -Einstein Lorentzian para-Sasakian manifold M represents a Riemann soliton for the potential vector field V has constant divergence then either, M is of constant curvature 1 or, V is a strict infinitesimal contact transformation.

A note on gradient solitons on two classes of almost Kenmotsu manifolds

Abstract: The purpose of the article is to characterize \textbf{gradient $(m,\rho)$-quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper.

Geometry of paracontact metric as an almost Yamabe solitons

Abstract: In this offering exposition, we intend to study paracontact metric manifold [Formula: see text] admitting almost Yamabe solitons. First, for a general paracontact metric manifold, it is proved that [Formula: see text] is Killing if the vector field [Formula: see text] is an infinitesimal contact transformation and that [Formula: see text] is [Formula: see text]-paracontact if [Formula: see text] is collinear with Reeb vector field. Second, we proved that a [Formula: see text]-paracontact manifold admitting a Yamabe gradient soliton is of constant curvature [Formula: see text] when [Formula: see text] and for [Formula: see text], the soliton is trivial and the manifold has constant scalar curvature. Moreover, for a paraSasakian manifold admitting a Yamabe soliton, we show that it has constant scalar curvature and [Formula: see text] is Killing when [Formula: see text]. Finally, we consider a paracontact metric [Formula: see text]-manifold with a non-trivial almost Yamabe gradient soliton. In the end, we construct two examples of paracontact metric manifolds with an almost Yamabe soliton.