∗-<i>η</i>-Ricci Soliton within the Framework of Sasakian Manifold

Dey, Santu; Roy, Soumendu

doi:10.1080/1726037x.2020.1856339

Cited by 29 publications

(21 citation statements)

References 9 publications

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“…In 2018, Ghosh and Patra [11] first studied the p -Ricci soliton on almost contact metric manifolds. Very recently, the p -Ricci soliton and its generalizations were investigated by Dey et al [6,12,13,[15][16][17][18][19][20][21]. The case of the p -Ricci soliton in a para-Sasakian manifold was treated by Prakasha and Veeresha in the study mentioned in reference [22].…”

Section: Introductionmentioning

confidence: 99%

∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

Dey

Turki

2022

Front. Phys.

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The goal of the present study is to study the ∗-η-Ricci soliton and gradient almost ∗-η-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. We demonstrate that a para-Kenmotsu metric as a ∗-η-Ricci soliton is an Einstein metric if the soliton vector field is contact. Next, we discuss the nature of the soliton and discover the scalar curvature when the manifold admits a ∗-η-Ricci soliton on a para-Kenmotsu manifold. After that, we expand the characterization of the vector field when the manifold satisfies the ∗-η-Ricci soliton. Furthermore, we characterize the para-Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies the gradient almost ∗-η-Ricci soliton.

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Section: Introductionmentioning

confidence: 99%

∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

Dey

Turki

2022

Front. Phys.

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“…Since the introduction of these geometric flows, the respective solitons and their generalizations have been a great centre of attention of many geometers viz. [3,5,17,18,19,20,21,22,23,24,25,26,27,29,30] who have provided new approaches to understand the geometry of different kinds of Riemannian manifold. Recently in 2019, S. Güler and M. Crasmareanu [10] introduced a new geometric flow which is a scalar combination of Ricci and Yamabe flow under the name Ricci-Yamabe map.…”

Section: Introductionmentioning

confidence: 99%

“…where µ is a constant and η is a 1-form on M . Recently * -η Ricci soliton, a generalization of η-Ricci soliton [5], has been defined by S. Dey and S. Roy [24], which can be given as,…”

Section: Introductionmentioning

confidence: 99%

$\ast$-$η$-Ricci-Yamabe solitons on $α$-Cosymplectic manifolds with a quarter-symmetric metric connection

Roy,

Dey,

Bhattacharyya

et al. 2021

Preprint

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The goal of the present paper is to deliberate certain types of metric such as * -η-Ricci-Yamabe soliton on α-Cosymplectic manifolds with respect to quarter-symmetric metric connection. Further, we have proved some curvature properties of α-Cosymplectic manifolds admitting quarter-symmetric metric connection. Here, we have shown the characteristics of the soliton when the manifold satisfies quartersymmetric metric connection on α-Cosymplectic manifolds. Later, we have acquired Laplace equation from * -η-Ricci-Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type in terms of quarter-symmetric metric connection. Next, we have developed the nature of the soliton when the vector field is conformal killing admitting quarter-symmetric metric connection. Finally, we present an example of a 5-dimensional α-cosymplectic metric as a * -η-Ricci-Yamabe soliton with respect to a quarter-symmetric metric connection to prove our results.

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“…For the Kenmotsu manifold possessing a gradient almost * -Ricci soliton they come up with: either the manifold is Einstein or the potential vector field is pointwise collinear with the characteristic vector field on some open set of the manifold. Further, Dey et al [7] have studied * -η-Ricci soliton on contact geometry. Being motivated from the well acclaimed results we consider * -conformal η-Ricci soliton and gradient almost * -conformal η-Ricci soliton in the framework of Kenmotsu manifolds.…”

Section: Introductionmentioning

confidence: 99%

$*$-Conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds

Sarkar¹,

Dey²

2021

Preprint

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The goal of our present paper is to deliberate * -conformal η-Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a * -conformal η-Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have evolved the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost *conformal η-Ricci soliton. Next, we have contrived * -conformal η-Ricci soliton admitting (κ, µ) ′ -almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to H n+1 (−4) × R n . Finally we have constructed some examples to illustrate the existence of * -conformal η-Ricci soliton, gradient almost * -conformal η-Ricci soliton on Kenmotsu manifold and (κ, µ) ′ -almost Kenmotsu manifolds.

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∗-η-Ricci Soliton within the Framework of Sasakian Manifold

Cited by 29 publications

References 9 publications

∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

$\ast$-$η$-Ricci-Yamabe solitons on $α$-Cosymplectic manifolds with a quarter-symmetric metric connection

$*$-Conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds

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