SOME TYPES OF  Η-Ricci SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

Singh, Abhishek; Kishor, Shyam

doi:10.22190/fumi1802217s

Cited by 11 publications

(9 citation statements)

References 8 publications

(9 reference statements)

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“…is called φ-conharmonically flat [13], where H is the conharmonic curvature tensor of M n . Let (M, φ, ξ, η, g) be a (2n+1) dimensional φ-conharmonically flat Sasakian manifold.…”

Section: Curvature Properties On Sasakian Manifold Satisfying * -Conf...mentioning

confidence: 99%

*-Conformal η-Ricci Soliton on Sasakian manifold

Roy,

Dey,

Bhattacharyya

et al. 2019

Preprint

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In this paper we study * -Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting * -Conformal η-Ricci soliton. We obtain some significant results on * -Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ, X) • S = 0, S(ξ, X) • R = 0, P (ξ, X) • S = 0, where P is Pseudo-projective curvature tensor.The conditions for * -Conformal η-Ricci soliton on φ-conharmonically flat and φ-projectively flat Sasakian manifolds have been obtained in this article. Lastly we give an example of 5-dimensional Sasakian manifolds satisfying * -Conformal η-Ricci soliton.

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“…is called φ-conharmonically flat [13], where H is the conharmonic curvature tensor of M n . Let (M, φ, ξ, η, g) be a (2n+1) dimensional φ-conharmonically flat Sasakian manifold.…”

Section: Curvature Properties On Sasakian Manifold Satisfying * -Conf...mentioning

confidence: 99%

*-Conformal η-Ricci Soliton on Sasakian manifold

Roy,

Dey,

Bhattacharyya

et al. 2019

Preprint

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“…Since the introduction of Ricci soliton and Yamabe soliton, many authors ( [21], [22], [9], [6], [8], [18]) have studied these solitons on contact manifolds.…”

Section: Introductionmentioning

confidence: 99%

Geometrical structure in a perfect fluid spacetime with conformal Ricci-Yamabe soliton

Roy¹,

Dey²,

Bhattacharyya³

2021

Preprint

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The present paper is to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci-Yamabe metric and conformal η-Ricci-Yamabe metric. Here we have delineated the conditions for conformal Ricci-Yamabe soliton to be expanding, steady or shrinking. Later, we have acquired Laplace equation from conformal η-Ricci-Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Lastly, we have designated perfect fluid with Robertson-Walker spacetime and some applications of physics and gravity.

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“…Recently an η-Ricci soliton has been studied by several authors such as [3,5,16,20,8,4] and they found many interesting geometric properties.…”

Section: Introductionmentioning

confidence: 99%

Eta-Ricci Solitons on Lorentzian Para-Kenmotsu Manifolds

2021

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The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $R\cdot S=0$. Further, we obtain results for $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $\eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $\eta$-quasi-conformally semi-symmetric, $\eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $\eta$-Ricci solitons.

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SOME TYPES OF Η-Ricci SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

Cited by 11 publications

References 8 publications

*-Conformal η-Ricci Soliton on Sasakian manifold

*-Conformal η-Ricci Soliton on Sasakian manifold

Geometrical structure in a perfect fluid spacetime with conformal Ricci-Yamabe soliton

Eta-Ricci Solitons on Lorentzian Para-Kenmotsu Manifolds

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