A Kenmotsu metric as a conformal $\eta$-Einstein soliton

Roy, Soumendu; Dey, Santu; Bhattacharyya, Arindam

doi:10.15330/cmp.13.1.110-118

Cited by 25 publications

(14 citation statements)

References 3 publications

(3 reference statements)

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“…) where ∇ denotes the Riemannian connection of g. In a Kenmotsu manifold the following relations hold ( [1], [29]):…”

Section: Preliminariesmentioning

confidence: 99%

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Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Dey¹,

Roy²

2021

Preprint

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The goal of the current paper is to characterize * -k-Ricci-Yamabe soliton within the framework on Kenmotsu manifolds. Here, we have shown the nature of the soliton and find the scalar curvature when the manifold admitting * -k-Ricci-Yamabe soliton on Kenmotsu manifold. Next, we have evolved the characterization of the vector field when the manifold satisfies * -k-Ricci-Yamabe soliton. Also we have embellished some applications of vector field as torse-forming in terms of * -k-Ricci-Yamabe soliton on Kenmotsu manifold. Then, we have studied gradient * -η-Einstein soliton to yield the nature of Riemannian curvature tensor. We have developed an example of * -k-Ricci-Yamabe soliton on 5-dimensional Kenmotsu manifold to prove our findings.

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“…) where ∇ denotes the Riemannian connection of g. In a Kenmotsu manifold the following relations hold ( [1], [29]):…”

Section: Preliminariesmentioning

confidence: 99%

“…Since the introduction of Ricci soliton and Yamabe soliton, many authors ( [24], [25], [26], [29], [27], [14], [3], [9], [22]) have studied these solitons on contact manifolds.…”

Section: Introductionmentioning

confidence: 99%

Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Dey¹,

Roy²

2021

Preprint

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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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“…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%

$\ast$-$η$-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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A Kenmotsu metric as a conformal $\eta$-Einstein soliton

Cited by 25 publications

References 3 publications

Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on 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

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A Kenmotsu metric as a conformal $\eta$-Einstein soliton

Cited by 25 publications

References 3 publications

Geometry of $*$-$k$-Ricci-Yamabe soliton and gradient $*$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Geometry of $*$-$k$-Ricci-Yamabe soliton and gradient $*$-$k$-Ricci-Yamabe soliton on 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

Contact Info

Product

Resources

About

Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds

Geometry of $$-$k$-Ricci-Yamabe soliton and gradient $$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds