Ricci solitons and gradient Ricci solitons on $3$-dimensional normal almost contact metric manifolds

De, Uday Chand; Turan, Mine; Yıldız, Ahmet; De, Avik

doi:10.5486/pmd.2012.4947

Cited by 19 publications

(4 citation statements)

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“…If k < −1, we denote the two non-zero eigenvalues of h by ν and −ν respectively, where ν = √ −1 − k > 0. Furthermore, by Proposition 3.1 of [8] we also have ∇ ξ h ′ = −2h ′ . We need the following results from [15] for proving our main theorem.…”

Section: Resultsmentioning

confidence: 85%

“…Recently, Ricci solitons and gradient Ricci solitons on some kinds of three dimensional almost contact metric manifolds have been studied by many authors. For instances, Ricci solitons and gradient Ricci solitons on three-dimensional normal almost contact metric manifolds are investigated in [8] and three-dimensional trans-Sasakian manifolds are considered in [14]. Moreover, a complete classification of Ricci solitons on three-dimensional Kenmotsu manifolds is given (see [10] and [7]).…”

Section: Introductionmentioning

confidence: 99%

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Ricci $ρ$-solitons on 3-dimensional $η$-Einstein almost Kenmotsu mandifolds

Azami,

Fasihi-Ramandi

2019

Preprint

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The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci ρ-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3dimensional almost Kenmotsu Einstein manifold M be a ρ-soliton, then M is a Kenmotsu manifold of constant sectional curvature −1 and the ρ-soliton is expanding, with λ = 2. 2010 Mathematics Subject Classification. 53Axx, 53Bxx.

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Section: Resultsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Ricci $ρ$-solitons on 3-dimensional $η$-Einstein almost Kenmotsu mandifolds

Azami,

Fasihi-Ramandi

2019

Preprint

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“…When f is a constant map, a gradient Ricci-harmonic soliton turns into a gradient Ricci soliton [8]. For details about Ricci and gradient Ricci solitons see also [14][15][16][17][18][19] and [20].…”

Section: Introductionmentioning

confidence: 99%

On sequential warped product manifolds admitting gradient Ricci-harmonic solitons

Karaca

Özgür

2023

Phys. Scr.

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“…Quite a long while prior, in [14], Olszak explored the three dimensional normal almost contact metric (briefly, acm) manifolds mentioning several examples. After the citation of [14], in recent years normal acm manifolds have been studied by numerous eminent geometers (see, [7], [8], [9], [10] and references contained in those).…”

Section: Introductionmentioning

confidence: 99%

A note on Almost Riemann Soliton and gradient almost Riemann soliton

De¹,

De²

2020

Preprint

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The quest of the offering article is to investigate almost Riemann soliton and gradient almost Riemann soliton in a non-cosymplectic normal almost contact metric manifold M 3 . Before all else, it is proved that if the metric of M 3 is Riemann soliton with divergence-free potential vector field Z, then the manifold is quasi-Sasakian and is of constant sectional curvature -λ, provided α, β = constant. Other than this, it is shown that if the metric of M 3 is ARS and Z is pointwise collinear with ξ and has constant divergence, then Z is a constant multiple of ξ and the ARS reduces to a Riemann soliton, provided α, β =constant. Additionally, it is established that if M 3 with α, β = constant admits a gradient ARS (γ, ξ, λ), then the manifold is either quasi-Sasakian or is of constant sectional curvature −(α 2 − β 2 ). At long last, we develop an example of M 3 conceding a Riemann soliton.

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Ricci solitons and gradient Ricci solitons on $3$-dimensional normal almost contact metric manifolds

Cited by 19 publications

References 0 publications

Ricci $ρ$-solitons on 3-dimensional $η$-Einstein almost Kenmotsu mandifolds

Ricci $ρ$-solitons on 3-dimensional $η$-Einstein almost Kenmotsu mandifolds

On sequential warped product manifolds admitting gradient Ricci-harmonic solitons

A note on Almost Riemann Soliton and gradient almost Riemann soliton

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