Some Results on Ricci Almost Solitons

Deshmukh, Sharief; Alsodais, Hana; Turki, Nasser Bin

doi:10.3390/sym13030430

Cited by 8 publications

(7 citation statements)

References 20 publications

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“…The preceding studies show that by selecting a suitable soliton vector field [10,[12][13][14][15][16], we can achieve important geometric findings. In this regard, a vector field created by the gradient of the height function from the immersion has already proven to be a rich source for producing examples of soliton fields.…”

Section: Discussionmentioning

confidence: 97%

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Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

et al. 2021

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In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics.

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Section: Discussionmentioning

confidence: 97%

“…Many theoretical aspects of conformal and homothetic (β = const) transformations can be found, for example in [8,9]. Utilizing Koszul's formula [10,11], we obtain the following for a vector field ζ on M:…”

Section: Preliminariesmentioning

confidence: 99%

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

et al. 2021

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“…In the geometry of a Ricci almost soliton, an important question is: under what conditions a Ricci almost soliton is trivial (Einstein)? Several results are proved in finding conditions under which a compact Ricci almost soliton is trivial, see details in [1,9,8,11,17]. Note that a ρ-Einstein almost soliton is a generalization of an Einstein manifold, Ricci soliton, Ricci almost soliton as well as ρ-Einstein soliton; therefore, the following question arises: Under what conditions a ρ-Einstein almost soliton on a K-contact manifold is trivial (Einstein)?…”

Section: Remark 12 One May Ask: Under What Conditions the Above Resul...mentioning

confidence: 99%

“…In recent years the pioneering works of R. Hamilton [14] and G. Perelman [18] towards the solution of the Poincaré conjecture have produced a flourishing activity in the research of self-similar solutions, or solitons, of the Ricci flow. For more details on Ricci solitons, we refer to the reader to [1,9,11,12,13,17,20]. In general, Bourguignon [4] introduced a perturbed version of the Ricci flow on an n-dimensional Riemannian manifold (M, g), which satisfies the following evolution equation [4] considered a geometric flow of the following type:…”

Section: Introductionmentioning

confidence: 99%

Some characterizations of -Einstein solitons on Sasakian manifolds

Patra¹

2022

Can. Math. Bull.

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The $\rho $ -Einstein soliton is a self-similar solution of the Ricci–Bourguignon flow, which includes or relates to some famous geometric solitons, for example, the Ricci soliton and the Yamabe soliton, and so on. This paper deals with the study of $\rho $ -Einstein solitons on Sasakian manifolds. First, we prove that if a Sasakian manifold M admits a nontrivial $\rho $ -Einstein soliton $(M,g,V,\lambda )$ , then M is $\mathcal {D}$ -homothetically fixed null $\eta $ -Einstein and the soliton vector field V is Jacobi field along trajectories of the Reeb vector field $\xi $ , nonstrict infinitesimal contact transformation and leaves $\varphi $ invariant. Next, we find two sufficient conditions for a compact $\rho $ -Einstein almost soliton to be trivial (Einstein) under the assumption that the soliton vector field is an infinitesimal contact transformation or is parallel to the Reeb vector field $\xi $ .

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“…Many researchers also analyzed perfect fluid spacetime with different solitons. For further information, read [23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

f(R,T)-Gravity Model with Perfect Fluid Admitting Einstein Solitons

Siddiqi

Chaubey²,

Khan

2021

Mathematics

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f(R,T)-gravity is a generalization of Einstein’s field equations (EFEs) and f(R)-gravity. In this research article, we demonstrate the virtues of the f(R,T)-gravity model with Einstein solitons (ES) and gradient Einstein solitons (GES). We acquire the equation of state of f(R,T)-gravity, provided the matter of f(R,T)-gravity is perfect fluid. In this series, we give a clue to determine pressure and density in radiation and phantom barrier era, respectively. It is proved that if a f(R,T)-gravity filled with perfect fluid admits an Einstein soliton (g,ρ,λ) and the Einstein soliton vector field ρ of (g,ρ,λ) is Killing, then the scalar curvature is constant and the Ricci tensor is proportional to the metric tensor. We also establish the Liouville’s equation in the f(R,T)-gravity model. Next, we prove that if a f(R,T)-gravity filled with perfect fluid admits a gradient Einstein soliton, then the potential function of gradient Einstein soliton satisfies Poisson equation. We also establish some physical properties of the f(R,T)-gravity model together with gradient Einstein soliton.

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Some Results on Ricci Almost Solitons

Cited by 8 publications

References 20 publications

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Some characterizations of -Einstein solitons on Sasakian manifolds

f(R,T)-Gravity Model with Perfect Fluid Admitting Einstein Solitons

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