On N(κ)-Contact Metric Manifolds Satisfying Certain Curvature Conditions

De, Avik; Jun, Jae-Bok

doi:10.5666/kmj.2011.51.4.457

Cited by 7 publications

(5 citation statements)

References 8 publications

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“…for any vector fields X, Y where R is the Riemannian curvature tensor and S is the Ricci tensor. N (k)-contact metric manifolds have been studied by several authors such as ( [6], [13], [14]) and many others.…”

Section: Preliminariesmentioning

confidence: 99%

*- Critical point equation on N(k)-contact manifolds

Dey¹,

Majhi²

2020

MIF

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The object of the present paper is to characterize N (k)-contact metric manifolds satisfying the * -critical point equation. It is proved that, if (g, λ) is a non-constant solution of the * -critical point equation of a non-compact N (k)-contact metric manifold, then (1) the manifold M is locally isometric to the Riemannian product of a flat (n + 1)-dimensional manifold and an n-dimensional manifold of positive curvature 4 for n > 1 and flat for n = 1, (2) the manifold is * -Ricci flat and (3) the function λ is harmonic. The result is also verified by an example.2000 Mathematics Subject Classification: 53C25, 53C15.

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Section: Preliminariesmentioning

confidence: 99%

*- Critical point equation on N(k)-contact manifolds

Dey¹,

Majhi²

2020

MIF

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“…for any vector fields X, Y on M , where R is the Riemann curvature tensor. For further details on N (k)-contact metric manifolds, we refer the reader to go through thereferences ( [5], [14], [15]) and references therein.…”

Section: Preliminariesmentioning

confidence: 99%

$N(k)$-contact metric as $\ast$-conformal Ricci soliton

Dey¹,

Majhi²

2020

Preprint

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The aim of this paper is characterize a class of contact metric manifolds admitting * -conformal Ricci soliton. It is shown that if a (2n + 1)-dimensional N (k)-contact metric manifold M admits * -conformal Ricci soliton or * -conformal gradient Ricci soliton, then the manifold M is * -Ricci flat and locally isometric to the Riemannian of a flat (n + 1)-dimensional manifold and an n-dimensional manifold of constant curvature 4 for n > 1 and flat for n = 1. Further, for the first case, the soliton vector field is conformal and for the * -gradient case, the potential function f is either harmonic or satisfy a Poisson equation. Finally, an example is presented to support the results.

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“…Contact metric manifolds have also been studied by several authors ( [4], [10], [11], [12], [13], [21], [22], [23], [25], and many others).…”

Section: Preliminariesmentioning

confidence: 99%

Beta-almost Ricci solitons on Sasakian 3-manifolds

Majhi

Kar

2019

Cubo

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In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field. Among others we prove that a βalmost Ricci soliton whose potential vector field is a contact vector field on a Sasakian 3-manifold is shrinking, Einstein and non-trivial. Moreover, we prove that this type of manifolds are isometric to a sphere of radius √ 7. RESUMEN En este artículo caracterizamos las 3-variedades Sasakianas que admiten solitones βcasi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto. Entre otros, probamos que un solitón β-casi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto en una 3-variedad Sasakiana se contrae, es Einstein y no trivial. Más aún, probamos que este tipo de variedades son isométricas a una esfera de radio √ 7.

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On N(κ)-Contact Metric Manifolds Satisfying Certain Curvature Conditions

Cited by 7 publications

References 8 publications

*- Critical point equation on N(k)-contact manifolds

*- Critical point equation on N(k)-contact manifolds

$N(k)$-contact metric as $\ast$-conformal Ricci soliton

Beta-almost Ricci solitons on Sasakian 3-manifolds

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