Generalized Quasi-Einstein Manifolds in Contact Geometry

Ünal, İ̇nan

doi:10.3390/math8091592

Cited by 4 publications

(5 citation statements)

References 24 publications

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“…Presented author worked on normal metric contact pair manifolds under some flatness conditions [13]. Also he 334 has presented some applications of generalized quasi-Einstein manifolds in contact geometry [14].…”

Section: Declaration Of Ethical Standardsmentioning

confidence: 99%

“…for all vector fields 12 , XX on M and  is non-zero scalar [14]. The following lemma comes from the decomposition of TM : Lemma 2.4.…”

Section: T Resp T Ffmentioning

confidence: 99%

“…H [14]. The concircular curvature tensor on Riemannian manifold was defined by Yano in [15].…”

Section: T Resp T Ffmentioning

confidence: 99%

“…NMCP MANIFOLDS A Riemann manifold is called a locally symmetric or a semi-symmetric manifold if .0  RR [14]. The contact manifolds are characterized by using semi-symmetry properties.…”

Section: Some Semi-symmetry Conditions Onmentioning

confidence: 99%

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On Metric Contact Pairs with Certain Semi-Symmetry Conditions

Ünal

2021

Politeknik Dergisi

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 Some significant contributions to the Riemannian geometry of contact pair manifolds were obtained.  Semi-symmetry conditions on Riemannian and Ricci curvature tensors were considered for normal metric contact pair manifolds.  Many classifications were given based on the semi-symmetry conditions of the concircular curvature tensor. Aim The aim of this paper is to study on the normal metric contact pair manifolds under some semisymmetry conditions. Design & Methodology The theoretical methodology of mathematics was used to obtain results. Originality All obtained results are original. They could be used for future works about contact pair geometry. Findings Normal metric contact pair manifolds are classified as a generalized quasi-Einstein manifold with certain semi-symmetry conditions. Conclusion It is seen that normal metric contact pair manifold could be special case of generalized quasi-Einstein manifolds which arises from general relativity.

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Section: Declaration Of Ethical Standardsmentioning

confidence: 99%

“…for all vector fields 12 , XX on M and  is non-zero scalar [14]. The following lemma comes from the decomposition of TM : Lemma 2.4.…”

Section: T Resp T Ffmentioning

confidence: 99%

“…H [14]. The concircular curvature tensor on Riemannian manifold was defined by Yano in [15].…”

Section: T Resp T Ffmentioning

confidence: 99%

“…NMCP MANIFOLDS A Riemann manifold is called a locally symmetric or a semi-symmetric manifold if .0  RR [14]. The contact manifolds are characterized by using semi-symmetry properties.…”

Section: Some Semi-symmetry Conditions Onmentioning

confidence: 99%

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On Metric Contact Pairs with Certain Semi-Symmetry Conditions

Ünal

2021

Politeknik Dergisi

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“…Here α, β are scalars and u k is a 1-form [12][13][14][15][16][17][18]. A perfect fluid spacetime is pictured as a Lorentzian quasi-Einstein manifold given that u k is a unit time-like vector field [14,19,20].…”

Section: Introductionmentioning

confidence: 99%

A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor

Shenawy

Mantica²,

Molinari

et al. 2022

Mathematics

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Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a λ,n+m-Einstein manifold M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, M,g,w reduces to a perfect fluid manifold if φ=−m∇lnw is a φRic-vector field on M and to an Einstein manifold if ψ=∇w is a ψRic-vector field on M. Some consequences of these results are considered.

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A study of conformal almost Ricci solitons on Kenmotsu manifolds

Sarkar

Dey

Bhattacharyya

2022

Int. J. Geom. Methods Mod. Phys.

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The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is [Formula: see text]-Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of [Formula: see text] is pointwise collinear with the Reeb vector field or the manifold becomes [Formula: see text]-Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold.

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Generalized Quasi-Einstein Manifolds in Contact Geometry

Cited by 4 publications

References 24 publications

On Metric Contact Pairs with Certain Semi-Symmetry Conditions

On Metric Contact Pairs with Certain Semi-Symmetry Conditions

A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor

A study of conformal almost Ricci solitons on Kenmotsu manifolds

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