Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds

Vanlı, Aysel Turgut; Ünal, İ̇nan

doi:10.1142/s0219887817500670

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…A concircularly flat spacetime is of constant curvature. As a result, the deviation of a spacetime from constant curvature is measured by the concircular curvature tensor M. Researchers have shown the curial role of the concircular curvature tensor in mathematics and physics (for example, see [2][3][4][5][6] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Shenawy

Abu-Donia

et al. 2022

Front. Phys.

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The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

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Section: Introductionmentioning

confidence: 99%

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Shenawy

Abu-Donia

et al. 2022

Front. Phys.

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“…Conformal and concircular curvature tensors on contact manifolds have been studied in [23][24][25]. M-projective curvature tensor on manifolds with different structures studied by many authors [26][27][28].…”

Section: Theoremmentioning

confidence: 99%

“…Let M be a M-projectively flat normal metric contact pair manifold , then, from (25), M is conformally flat if and only if…”

Section: Theorem 11mentioning

confidence: 99%

Generalized Quasi-Einstein Manifolds in Contact Geometry

Ünal

2020

Mathematics

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In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.

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“…De et al [27] showed that, in a conharmonically flat spacetime with cyclic parallel Ricci tensor, the energy-momentum tensor is cyclic parallel and conversely. The flatness conditions of the conharmonic curvature tensor on normal complex contact metric manifolds were studied by Vanli and Unal [28]. Yildirim [29] proved that certain types of complex κµ spaces cannot be conharmonically flat.…”

Section: Introductionmentioning

confidence: 99%

How Extra Symmetries Affect Solutions in General Relativity

Беешам

Makhanya

2020

Universe

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To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cause the problem to become somewhat trivial. As a typical example to illustrate this, the effects of conharmonic flatness are studied and applied to Friedmann–Lemaitre–Robertson–Walker spacetime. Hence, we need to impose some symmetry to make the problem tractable, but not too much so as to make it too simple.

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Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds

Abstract: Conformal, concircular, quasi-conformal and conharmonic curvature tensors play an important role in Riemannian geometry. In this paper, we study on normal complex contact metric manifolds under flatness conditions of these tensors.

Cited by 11 publications

References 12 publications

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Spacetimes Admitting Concircular Curvature Tensor in f(R) Gravity

Generalized Quasi-Einstein Manifolds in Contact Geometry

How Extra Symmetries Affect Solutions in General Relativity

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