Solitons of Kählerian space-time manifolds

Praveena, M. M.; Bagewadi, C. S.; Krishnamurthy, M. R.

doi:10.1142/s0219887821500213

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…In an almost pseudo symmetric pseudo-projectively flat Lorentzian Kähler spacetime manifold admitting Einstein field equation with cosmological constant, the h-almost conformal Ricci-Bourguignon soliton (g, ξ, h, µ, Λ) for the dark fluid is shrinking, if p > (κρ 18. In an almost pseudo symmetric pseudo-projectively flat Lorentzian Kähler spacetime manifold admitting Einstein field equation with cosmological constant, the h-almost conformal Ricci-Bourguignon soliton (g, ξ, h, µ, Λ) for the dust fluid is shrinking, if p 19. In an almost pseudo symmetric pseudo-projectively flat Lorentzian Kähler spacetime manifold admitting Einstein field equation with cosmological constant, the h-almost conformal Ricci-Bourguignon soliton (g, ξ, h, µ, Λ) for the radiation fluid is shrinking, if p…”

Section: Definition 34 ([17]mentioning

confidence: 99%

“…In 2020, Siddiqi and Siddiqui [20] investigated the geometrical features of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal η-Ricci soliton with torse-forming vector field ξ. Praveena et al [19] published their study on solitons of almost pseudo symmetric Kählerian space-time manifold. In the paper they showed that solitons are steady, expanding or shrinking under different relations of isotropic pressure, the cosmological constant, energy density and gravitational constant.…”

Section: Introductionmentioning

confidence: 99%

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On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime

Pahan

2024

ACUTM

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The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton.

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Section: Definition 34 ([17]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime

Pahan

2024

ACUTM

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“…We find that the values of the cosmological constant, the energy density, the gravitational constant, and the pressure at an isotropic pressure of 25 all affect the stability, growth, and shrinking of solitons. [ 13] RESEARCH METHODOLOGY Secondary sources, such as books, educational and development publications, government papers, and print and online reference materials, were our primary means of acquiring knowledge about the Kahlerian Einstein manifold.…”

Section: Review Of Literaturementioning

confidence: 99%

A Study on Manifold Kaehleriain Space

Singh¹,

Singh²

2022

IJMCR

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This work delves into the space-time theory of the 4-dimensional Kaehler manifold. Since the isotropic pressure, energy density, and energy momentum tensor all vanish in a perfect fluid Kaehler space-time manifold, we have established that this space-time manifold is an Einstein manifold and studied the Einstein equation with a cosmological constant in it. Finally, we demonstrated that, on a conformally flat, perfectly fluid Kaehler space-time manifold, the velocity vector field is infinitesimally spatially isotropic. Ideal fluid dilution to the point where only Ricci and minimal symmetry hold. We have proven that Kaehler space-time manifolds have either 0 scalar curvature or a connection between the respective rho and alpha vector fields via g(rho,alpha) = 4. To conclude, we have proved that a Kaehler space-time manifold cannot have both perfect fluidity and non-zero scalar curvature (weak Ricci symmetry).

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“…Also, Conformal Ricci soliton in perfect fluid spacetime [23] is studied. Praveena et al [20] studied solitons in Kählerian space-time manifolds. As Ricci-Yamabe soliton is a scalar combination of Ricci and Yamabe soliton, it is fruitful to study it in the context of perfect fluid spacetime and obtain results that generalize the previously known results in perfect fluid spacetime.…”

Section: Introductionmentioning

confidence: 99%

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Singh

Khatri

2021

Afr. Mat.

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In this paper, we studied the geometrical aspects of a perfect fluid spacetime with torseforming vector field ξ under certain curvature restrictions, and Ricci-Yamabe soliton and η-Ricci-Yamabe soliton in a perfect fluid spacetime. Conditions for the Ricci-Yamabe soliton to be steady, expanding or shrinking are also given. Moreover, when the potential vector field ξ of η-Ricci-Yamabe soliton is of gradient type, we derive a Poisson equation and also looked at its particular cases. Lastly, a non-trivial example of perfect fluid spacetime admitting η-Ricci-Yamabe soliton is constructed.

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Solitons of Kählerian space-time manifolds

Cited by 4 publications

References 14 publications

On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime

On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime

A Study on Manifold Kaehleriain Space

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

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