scholarly journals Geometry of α-Cosymplectic Metric as ∗-Conformal η-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2189
Author(s):  
Pengfei Zhang ◽  
Yanlin Li ◽  
Soumendu Roy ◽  
Santu Dey
Keyword(s):  
Conformal Killing ◽  
Soliton Equation ◽  
Potential Vector ◽  
Research Article ◽  
Cosymplectic Manifolds ◽  
Metric Connection ◽  
Gradient Type ◽  
Yamabe Solitons ◽  
Yamabe Soliton ◽  
Potential Vector Field

The outline of this research article is to initiate the development of a ∗-conformal η-Ricci–Yamabe soliton in α-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of α-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional α-cosymplectic metric as a ∗-conformal η-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.

Almost quasi-Yamabe solitons on almost cosymplectic manifolds

2020 ◽  
Vol 17 (05) ◽  
pp. 2050070
Author(s):  
Xiaomin Chen
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Cosymplectic Manifolds ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Yamabe Soliton ◽  
Potential Vector Field

In this paper, we study almost cosymplectic manifolds admitting almost quasi-Yamabe solitons [Formula: see text]. First, we prove that an almost cosymplectic [Formula: see text]-manifold is locally isomorphic to a Lie group if [Formula: see text] is a nontrivial closed quasi-Yamabe soliton. Next, we consider an almost [Formula: see text]-cosymplectic manifold admitting a nontrivial almost quasi-Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector filed. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector filed, we also obtain two results. Finally, for a closed almost quasi-Yamabe soliton on compact [Formula: see text]-cosymplectic manifolds, we prove that it is trivial if [Formula: see text] is nonnegative, where [Formula: see text] is the scalar curvature.

scholarly journals A Note on LP -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sunil Kumar Yadav ◽  
D. L. Suthar ◽  
Biniyam Shimelis
Keyword(s):  
Vector Field ◽  
Sasakian Manifolds ◽  
Potential Vector ◽  
Metric Connection ◽  
Yamabe Solitons ◽  
Potential Vector Field

We categorize almost quasi-Yamabe solitons on LP -Sasakian manifolds and their CR -submanifolds whose potential vector field is torse-forming, admitting a generalized symmetric metric connection of type α , β . Finally, a nontrivial example is provided to confirm some of our results.

Ricci almost soliton and almost Yamabe soliton on Kenmotsu manifold

2020 ◽  
pp. 2150130
Author(s):  
Amalendu Ghosh
Keyword(s):  
Warped Product ◽  
Ricci Soliton ◽  
Product Spaces ◽  
Kenmotsu Manifold ◽  
Potential Vector ◽  
Dimension Formula ◽  
Yamabe Solitons ◽  
Warped Product Spaces ◽  
Yamabe Soliton ◽  
Potential Vector Field

We prove that a Ricci almost soliton on a Kenmotsu manifold of dimension [Formula: see text] reduces to an expanding Ricci soliton satifying certain condition on the potential vector field or on the soliton function. Next, we show that any Ricci almost soliton on a Kenmotsu manifold is trivial (Einstein) if the soliton vector leaves the contact form [Formula: see text] invariant. Finally, we classify (locally) a Kenmotsu manifold admitting an almost Yamabe soliton. Some examples have been constructed of almost Yamabe solitons on different class of warped product spaces.

scholarly journals Imperfect Fluid Generalized Robertson Walker Spacetime Admitting Ricci-Yamabe Metric

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ali H. Alkhaldi ◽  
Mohd Danish Siddiqi ◽  
Meraj Ali Khan ◽  
Lamia Saeed Alqahtani
Keyword(s):  
Vector Field ◽  
Potential Function ◽  
Poisson Equation ◽  
Sufficient Conditions ◽  
Potential Vector ◽  
Imperfect Fluid ◽  
Gradient Type ◽  
Necessary And Sufficient ◽  
Yamabe Soliton ◽  
Potential Vector Field

In the present paper, we investigate the nature of Ricci-Yamabe soliton on an imperfect fluid generalized Robertson-Walker spacetime with a torse-forming vector field ξ . Furthermore, if the potential vector field ξ of the Ricci-Yamabe soliton is of the gradient type, the Laplace-Poisson equation is derived. Also, we explore the harmonic aspects of η -Ricci-Yamabe soliton on an imperfect fluid GRW spacetime with a harmonic potential function ψ . Finally, we examine necessary and sufficient conditions for a 1 -form η , which is the g -dual of the vector field ξ on imperfect fluid GRW spacetime to be a solution of the Schrödinger-Ricci equation.

scholarly journals Yamabe Solitons with potential vector field as torse forming

Cubo (Temuco) ◽  
2018 ◽  
Vol 20 (3) ◽  
pp. 37-47
Author(s):  
Yadab ChandraMandal ◽  
Shyamal Kumar Hui
Keyword(s):  
Vector Field ◽  
Potential Vector ◽  
Yamabe Solitons ◽  
Potential Vector Field

The k-almost Yamabe solitons and almost coKähler manifolds

2021 ◽  
pp. 2150179
Author(s):  
Xiaomin Chen ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Potential Vector Field

In this paper, we study almost coKähler manifolds admitting [Formula: see text]-almost Yamabe solitons [Formula: see text]. First, we obtain a classification of almost coKähler [Formula: see text]-manifolds admitting nontrivial closed [Formula: see text]-almost Yamabe solitons. Next, we consider an almost [Formula: see text]-coKähler manifold admitting a nontrivial [Formula: see text]-almost Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector field. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector field, we also obtain two results.

Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime

2020 ◽  
Vol 17 (06) ◽  
pp. 2050083
Author(s):  
Mohd. Danish siddiqi ◽  
Shah Alam Siddiqui
Keyword(s):  
Vector Field ◽  
Perfect Fluid ◽  
Geometrical Structure ◽  
Ricci Soliton ◽  
Soliton Equation ◽  
Potential Vector ◽  
Laplacian Equation ◽  
Gradient Type ◽  
Perfect Fluid Spacetime ◽  
Text Condition

In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.

scholarly journals On warped product gradient η-Ricci solitons

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5791-5801 ◽  
Author(s):  
Adara Blaga
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Warped Product ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Product Manifold ◽  
Potential Vector ◽  
Warped Product Manifold ◽  
Gradient Type ◽  
Potential Vector Field

If the potential vector field of an ?-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by f . We give a way to construct a gradient ?-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature.

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