A note on almost co-Kähler manifolds

De, Uday Chand; Chaubey, Sudhakar K.; Suh, Young Jin

doi:10.1142/s0219887820501534

Cited by 32 publications

(8 citation statements)

References 33 publications

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“…This soliton is named shrinking, steady or expanding according as β 2 < 0, β 2 = 0 or β 2 > 0, respectively. Few interesting results of this solitons have been established in ( [11], [18]).…”

Section: Introductionmentioning

confidence: 93%

Characterization of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons

De¹,

De²

2022

Preprint

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The prime object of this article is to study the perfect fluid spacetimes obeying f (R)-gravity, when B-Ricci solitons, gradient B-Ricci solitons, gradient Einstein Solitons and gradient m-quasi Einstein solitons are its metrics. At first, the existence of B-Ricci solitons and gradient Einstein Solitons are proved by two non-trivial example. We establish conditions for which the B-Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying f (R)-gravity, when the potential vector field of B-Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient B-Ricci solitons, gradient Einstein Solitons and gradient m-quasi Einstein solitons in f (R)-gravity, respectively. As a result, we establish some significant theorems about dark matter era.

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Section: Introductionmentioning

confidence: 93%

Characterization of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons

De¹,

De²

2022

Preprint

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“…In addition, if M 2n+ is normal, then the manifold M 2n+1 is called co-Kähler manifold. An (almost) co-Kähler manifold is nothing but an (almost) cosymplectic manifold defined by Blair [3] and studied by several authors (see [1], [4]- [8], [11]- [13], [17,18] [23], [27]- [32]).…”

Section: Almost Co-kähler Manifoldsmentioning

confidence: 99%

Riemann solitons on almost co-Kähler manifolds

Biswas

Chen

2022

Filomat

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The aim of the present paper is to characterize almost co-K?hler manifolds whose metrics are the Riemann solitons. At first we provide a necessary and sufficient condition for the metric of a 3-dimensional manifold to be Riemann soliton. Next it is proved that if the metric of an almost co-K?hler manifold is a Riemann soliton with the soliton vector field ?, then the manifold is flat. It is also shown that if the metric of a (?, ?)-almost co-K?hler manifold with ? < 0 is a Riemann soliton, then the soliton is expanding and ?, ?, ? satisfies a relation. We also prove that there does not exist gradient almost Riemann solitons on (?, ?)-almost co-K?hler manifolds with ? < 0. Finally, the existence of a Riemann soliton on a three dimensional almost co-K?hler manifold is ensured by a proper example.

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“…In addition, if N 2m+1 is normal, then the manifold N 2m+1 is called a co-Kähler manifold. An ackm is the same as an almost cosymplectic manifold [28] and investigated by several geometers [7,23,[29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Preliminariesmentioning

confidence: 99%

η-∗-Ricci Solitons and Almost co-Kähler Manifolds

Sardar

Khan

2021

Mathematics

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The subject of the present paper is the investigation of a new type of solitons, called η-∗-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on ackm is obtained. Additionally, we classify the η-∗-Ricci solitons in (k,μ)-ackms. Next, we investigate (k,μ)-ackms admitting gradient η-∗-Ricci solitons. Finally, we construct two examples to illustrate our results.

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A note on almost co-Kähler manifolds

Cited by 32 publications

References 33 publications

Characterization of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons

Characterization of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons

Riemann solitons on almost co-Kähler manifolds

η-∗-Ricci Solitons and Almost co-Kähler Manifolds

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