Yamabe Solitons On (LCS)n -Manifolds

Roy, Soumendu; Dey, Santu; Bhattacharyya, Arindam

doi:10.1080/1726037x.2020.1868100

Cited by 23 publications

(16 citation statements)

References 7 publications

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“…Finally, taking into account ( 8), ( 13) and the vanishing of θ, θ * and ω for any cosymplectic B-metric manifold, we find the expressions of the Lee forms of the transformed manifold as in (14).…”

Section: The Case When the Given Manifold Is Cosymplecticmentioning

confidence: 99%

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Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

Manev¹

2022

Preprint

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A Yamabe soliton is defined on arbitrary almost contact Bmetric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the B-metric. An explicit 5dimensional example of a Lie group is given, which is characterized in relation to the obtained results.

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Section: The Case When the Given Manifold Is Cosymplecticmentioning

confidence: 99%

“…Many authors have studied the Yamabe soliton on different types of manifolds since the introduction of this concept (see e.g. [2,3,5,7,14]).…”

Section: Introductionmentioning

confidence: 99%

Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

Manev¹

2022

Preprint

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“…If λ is a smooth function then (1.2) is called almost Yamabe soliton [1]. Many authors such as [16], [17], [5], [7] have studied Yamabe solitons on some contact manifolds.…”

Section: Introductionmentioning

confidence: 99%

Conformal Yamabe soliton and $*$-Yamabe soliton with torse forming potential vector field

Roy,

Dey,

Bhattacharyya

2021

Preprint

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The goal of this paper is to study conformal Yamabe soliton and * -Yamabe soliton, whose potential vector field is torse forming. Here, we have characterized conformal Yamabe soliton admitting potential vector field as torse forming with respect to Riemannian connection, semi-symmetric metric connection and projective semi-symmetric connection on Riemannian manifold. We have also shown the nature of * -Yamabe soliton with torse forming vector field on Riemannian manifold admitting Riemannian connection. Lastly we have developed an example to corroborate some theorems regarding Riemannian connection on Riemannian manifold.

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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

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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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Yamabe Solitons On (LCS)_n -Manifolds

Cited by 23 publications

References 7 publications

Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

Conformal Yamabe soliton and $*$-Yamabe soliton with torse forming potential vector field

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

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