Almost Kenmotsu metric as a conformal Ricci soliton

Dey, Dibakar; Majhi, Pradip

doi:10.1090/ecgd/335

Cited by 15 publications

(6 citation statements)

References 22 publications

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“…In [4], Dileo and Pastore presented an example of a (2n + 1)-dimensional (k, µ) ′almost Kenmotsu manifold. In [3], the authors studied this for 5-dimensional case and obtained k = −2. We now mention the necessary results from that example to verify our result.…”

Section: Example Of a Shrinking Quasi Yamabe Solitonmentioning

confidence: 99%

Almost Kenmotsu metric as quasi Yamabe soliton

Dey,

Majhi

2020

Preprint

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In the present paper, we characterize a class of almost Kenmotsu manifolds admitting quasi Yamabe soliton. It is shown that if a (k, µ) ′ -almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, λ, α) with V pointwise collinear with ξ, then (1) V is a constant multiple of ξ, (2) V is a strict infinitesimal contact transformation and (3) (£ V h ′ )X = 0 for any vector field X. Finally an illustrative example is presented to support the result.

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Section: Example Of a Shrinking Quasi Yamabe Solitonmentioning

confidence: 99%

Almost Kenmotsu metric as quasi Yamabe soliton

Dey,

Majhi

2020

Preprint

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“…in [10] showed that if a Lorentzian α-Sasakian manifold admits conformal Ricci soliton and is Weyl conformally semi-symmetric, then the manifold is η-Einstein. Again in [9] it has been proved that a (k, µ)…”

Section: Introductionmentioning

confidence: 98%

Characteristics of conformal Ricci soliton on warped product spaces

Ganguly¹,

Basu²,

Bhattacharyya³

2021

Preprint

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Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual Riemannian product manifolds. First, we prove that if a warped product manifold admits conformal Ricci soliton then the base and the fiber also share the same property. In the next section the characterization of conformal Ricci solitons on warped product manifolds in terms of Killing and conformal vector fields has been studied. Next, we prove that a warped product manifold admitting conformal Ricci soliton with concurrent potential vector field is Ricci flat. Finally, an application of conformal Ricci soliton on a class of warped product spacetimes namely, generalized Robertson-Walker spacetimes has been discussed.

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“…Dey et.al. [8] studied conformal Ricci solitons on almost Kenmotsu manifolds. Siddiqui [22] studied conformal Ricci solitons of Lagrangian submanifolds in Kahler manifolds.…”

Section: Introductionmentioning

confidence: 99%

Conformal Ricci solitons on generalized (κ,μ)-space forms

Lone

Wani

2022

Int. J. Geom. Methods Mod. Phys.

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In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized [Formula: see text]-space forms. The conditions for the solitons to be shrinking, steady and expanding are derived in terms of conformal pressure [Formula: see text]. We show under what conditions a Ricci semi-symmetric generalized [Formula: see text]-space form equipped with a conformal Ricci soliton forms an Einstein manifold.

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Almost Kenmotsu metric as a conformal Ricci soliton

Cited by 15 publications

References 22 publications

Almost Kenmotsu metric as quasi Yamabe soliton

Almost Kenmotsu metric as quasi Yamabe soliton

Characteristics of conformal Ricci soliton on warped product spaces

Conformal Ricci solitons on generalized (κ,μ)-space forms

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