Gradient Ricci Almost Solitons on Two Classes of Almost Kenmotsu Manifolds

Wang, Yaning

doi:10.4134/jkms.j150416

Cited by 27 publications

(15 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[27], Barros-Riberiro [28], Sharma [29], Wang [30], and Duggal [31]. Following is a link between the CC symmetry of CPF-hypersurfaces and ARS and RS evolving equation (37) as α is a variable function or a constant.…”

Section: Proposition 3 (See [10]) a Vector Field ξ On A Semi-riemannian Manifold (M G) Is An Acv If And Only Ifmentioning

confidence: 99%

A New Class of Contact Pseudo Framed Manifolds with Applications

Duggal

2021

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M , g , f , λ , ξ by a real tensor field f of type 1,1 , a real function λ such that f 3 = λ 2 f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration.

show abstract

Section: Proposition 3 (See [10]) a Vector Field ξ On A Semi-riemannian Manifold (M G) Is An Acv If And Only Ifmentioning

confidence: 99%

A New Class of Contact Pseudo Framed Manifolds with Applications

Duggal

2021

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…Also, for an ARS-manifold, the vector V is conformal if and only if

\bar{g}

is Einstein. So far we have references [6, 15–18] on ARS manifolds.…”

Section: Almost Ricci Soliton Semi-riemannian Manifoldsmentioning

confidence: 99%

A New Class of Almost Ricci Solitons and Their Physical Interpretation

Duggal

2016

International Scholarly Research Notices

View full text Add to dashboard Cite

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u, μ, p, α, η, σ ij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems.

show abstract

“…In the last decade, a large number of papers were published regarding classi cation of Ricci solitons on almost contact manifolds. Among others, we refer the readers to [4][5][6][7], [8][9][10][11][12] and [13][14][15][16] for fruitful results on (almost) Ricci solitons on contact metric, (almost) Kenmotsu and (almost) cosymplectic manifolds, respectively. Recently, a new research interest has appeared regarding the so called *-Ricci soliton which is de ned by L V g + Ric * + λg = , (1.2) where V and λ still denote a vector eld (called the potential vector eld) and a constant (called the soliton constant).…”

Section: Introductionmentioning

confidence: 99%

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

Dai

Zhao

2019

Open Mathematics

View full text Add to dashboard Cite

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.

show abstract

Gradient Ricci Almost Solitons on Two Classes of Almost Kenmotsu Manifolds

Cited by 27 publications

References 19 publications

A New Class of Contact Pseudo Framed Manifolds with Applications

A New Class of Contact Pseudo Framed Manifolds with Applications

A New Class of Almost Ricci Solitons and Their Physical Interpretation

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

Contact Info

Product

Resources

About