Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector field

Chakraborty, Debabrata; Hui, Shyamal Kumar

doi:10.20852/ntmsci.2016320381

ntmsci

2016

DOI: 10.20852/ntmsci.2016320381

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Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector field

Debabrata Chakraborty¹,

Shyamal Kumar Hui²

Abstract: The present paper deals with the study of generalized Sasakian-space-forms whose metric is Ricci almost soliton with a conformal killing vector field. We obtain sufficient conditions of such type of Ricci almost solitons to be expanding, steady and shrinking respectively.

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Cited by 4 publications

References 22 publications

(24 reference statements)

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Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

Dey,

Hui,

Roy

et al. 2024

Int. J. Geom. Methods Mod. Phys.

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In this research paper, we determine the nature of conformal [Formula: see text]-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal [Formula: see text]-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal [Formula: see text]-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal [Formula: see text]-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form [Formula: see text], which is the [Formula: see text]-dual of the vector field [Formula: see text] on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.

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Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

Dey,

Hui,

Roy

et al. 2024

Int. J. Geom. Methods Mod. Phys.

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W-semisymmetric generalized Sasakian-space-forms

Chaubey¹,

Yadav

2019

Advances in Pure and Applied Mathematics

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AbstractWe set a definition of a {(0,2)}-type tensor on the generalized Sasakian-space-forms. The necessary and sufficient conditions for W-semisymmetric generalized Sasakian-space forms are studied. Certain results of the Ricci solitons, the Killing vector fields and the closed 1-form on the generalized Sasakian-space-forms are derived. We also verify our results by taking non-trivial examples of the generalized Sasakian-space-forms.

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A study on nearly recurrent generalized (k,μ)−space forms

Prasad,

Yadav

2024

Filomat

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Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector field

Abstract: The present paper deals with the study of generalized Sasakian-space-forms whose metric is Ricci almost soliton with a conformal killing vector field. We obtain sufficient conditions of such type of Ricci almost solitons to be expanding, steady and shrinking respectively.

Cited by 4 publications

References 22 publications

Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

Conformal η-Ricci–Bourguignon soliton in general relativistic spacetime

W-semisymmetric generalized Sasakian-space-forms

A study on nearly recurrent generalized (k,μ)−space forms

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