Journal ArticleDOI
Almost Kenmotsu $$(k,\mu )'$$ ( k , μ ) ′ -manifolds with Yamabe solitons
TLDR
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 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.read more
Citations
More filters
Journal ArticleDOI
Ricci-Yamabe solitons and 3-dimensional Riemannian manifolds
TL;DR: In this paper , the authors classify 3-dimensional Riemannian manifolds endowed with a special type of vector field if the metrices are Ricci-Yamabe solitons and gradient Ricci Yamabe Solitons, respectively.
Yamabe and riemann solitons on lorentzian para-sasakian manifolds
TL;DR: In this article , the authors studied Yamabe soliton and Riemann soliton on a 3D Lorentzian para-Sasakian manifold and proved that the soliton constant λ is always greater than zero with either τ = 2, or τ = 6, or λ = 6.
Journal ArticleDOI
A note on gradient solitons on two classes of almost Kenmotsu manifolds
TL;DR: In this paper , the authors characterize quasi-Einstein solitons within the framework of two classes of almost Kenmotsu manifolds, and consider an example to justify a result of their paper.
Journal ArticleDOI
Geometry of paracontact metric as an almost Yamabe solitons
TL;DR: In this paper , it was shown that a paracontact metric manifold admits an almost Yamabe gradient soliton and has constant scalar curvature, while the soliton is trivial and the manifold has constant curvature.
References
More filters
Journal ArticleDOI
Almost quasi-Yamabe solitons on almost cosymplectic manifolds
TL;DR: In this article, it was shown that an almost cosymplectic manifold admits almost quasi-Yamabe solitons (g,V,m,λ) and is locally isomorphic to a Lie manifold.
Journal ArticleDOI
A note on quasi-Yamabe solitons on contact metric manifolds
Chiranjib Dey,Uday Chand De +1 more
TL;DR: In this article, it was shown that if a contact metric manifold admits a quasi-Yamabe soliton whose soliton field is the V-Ric vector field, then the Ricci operator Q commutes with the (1, 1) tensor.
Journal ArticleDOI
Some results on (k, μ)′-almost Kenmotsu manifolds
Yaning Wang,Wenjie Wang +1 more
TL;DR: In this paper, the Weyl conformal curvature tensor and concircular curvatures tensor were studied on a (k, μ)′-almost Kenmotsu manifold M2n+1 of dimension greater than 3.
Some results on almost Kenmotsu manifolds
TL;DR: In this article, it was shown that for a -almost-Kenmotsu manifold with and, the tensor vanishes and every conformal vector field which leaves the curvature tensor invariant is Killing.
Related Papers (5)
Infinitely many solutions to the Yamabe problem on noncompact manifolds
Renato G. Bettiol,Paolo Piccione +1 more