scholarly journals On the h-almost Ricci soliton

2017 ◽  
Vol 114 ◽  
pp. 216-222 ◽  
Author(s):  
J.N. Gomes ◽  
Qiaoling Wang ◽  
Changyu Xia
Keyword(s):  
Ricci Soliton ◽  
Almost Ricci Soliton

scholarly journals A New Class of Almost Ricci Solitons and Their Physical Interpretation

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
K. L. Duggal
Keyword(s):  
Physical Model ◽  
Dynamic Properties ◽  
Fluid Velocity ◽  
General Relation ◽  
Ricci Soliton ◽  
Field Equations ◽  
Open Problems ◽  
Matter Tensor ◽  
Imperfect Fluid ◽  
Almost Ricci Soliton

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,σij) 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.

scholarly journals Gradient almost Ricci solitons on multiply warped product manifolds

2021 ◽  
Vol 13 (2) ◽  
pp. 386-394
Author(s):  
S. Günsen ◽  
L. Onat
Keyword(s):  
Potential Field ◽  
Warped Product ◽  
Einstein Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Product Manifold ◽  
Rigidity Result ◽  
Warped Product Manifold ◽  
Almost Ricci Soliton

In this paper, we investigate multiply warped product manifold \[M =B\times_{b_1} F_1\times_{b_2} F_2\times_{b_3} \ldots \times_{b_m} F_m\] as a gradient almost Ricci soliton. Taking $b_i=b$ for $1\leq i \leq m$ lets us to deduce that potential field depends on $B$. With this idea we also get a rigidity result and show that base is a generalized quasi-Einstein manifold if $\nabla b$ is conformal.

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

Almost Ricci solitons isometric to spheres

2019 ◽  
Vol 16 (05) ◽  
pp. 1950073 ◽  
Author(s):  
Sharief Deshmukh
Keyword(s):  
Lower Bound ◽  
Poisson Equation ◽  
Ricci Curvature ◽  
Unit Sphere ◽  
Potential Field ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Almost Ricci Soliton

We find a characterization of a sphere using a compact gradient almost Ricci soliton and the lower bound on the integral of Ricci curvature in the direction of potential field. Also, we use Poisson equation on a compact gradient almost Ricci soliton to find a characterization of the unit sphere.

scholarly journals A New Class of Contact Pseudo Framed Manifolds with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
K. L. Duggal
Keyword(s):  
Vector Field ◽  
Real Function ◽  
Tensor Field ◽  
Contact Manifold ◽  
Ricci Soliton ◽  
Contact Manifolds ◽  
Normal Contact ◽  
New Class ◽  
Almost Ricci Soliton ◽  
Characteristic Vector Field

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.

scholarly journals ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

2019 ◽  
Vol 69 (6) ◽  
pp. 1447-1458 ◽  
Author(s):  
Venkatesha ◽  
Devaraja Mallesha Naik ◽  
H. Aruna Kumara
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Potential Vector ◽  
Open Set ◽  
Kenmotsu Manifolds ◽  
Almost Ricci Soliton ◽  
Characteristic Vector Field ◽  
Potential Vector Field

Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

scholarly journals Almost $$*$$-Ricci soliton on paraKenmotsu manifolds

2019 ◽  
Vol 9 (3) ◽  
pp. 715-726 ◽  
Author(s):  
V. Venkatesha ◽  
H. Aruna Kumara ◽  
Devaraja Mallesha Naik
Keyword(s):  
Vector Field ◽  
Constant Curvature ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Almost Ricci Soliton ◽  
Potential Vector Field

Abstract We consider almost $$*$$ ∗ -Ricci solitons in the context of paracontact geometry, precisely, on a paraKenmotsu manifold. First, we prove that if the metric g of $$\eta $$ η -Einstein paraKenmotsu manifold is $$*$$ ∗ Ricci soliton, then M is Einstein. Next, we show that if $$\eta $$ η -Einstein paraKenmotsu manifold admits a gradient almost $$*$$ ∗ -Ricci soliton, then either M is Einstein or the potential vector field collinear with Reeb vector field $$\xi $$ ξ . Finally, for three-dimensional case we show that paraKenmotsu manifold is of constant curvature $$-1$$ - 1 . An illustrative example is given to support the obtained results.

Riemannian submersions whose total manifolds admit a Ricci soliton

2019 ◽  
Vol 16 (12) ◽  
pp. 1950196
Author(s):  
Şemsi̇ Eken Meri̇ç ◽  
Erol Kiliç
Keyword(s):  
Necessary Conditions ◽  
Riemannian Submersion ◽  
Ricci Soliton ◽  
Riemannian Submersions ◽  
Target Manifold ◽  
Almost Ricci Soliton

In this paper, we study Riemannian submersions whose total manifolds admit a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.

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