Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Alkhaldi, Ali H.; Laurian-Ioan, Pişcoran; Abolarinwa, Abimbola; Ali, Akram

doi:10.3390/sym13122362

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…As is well known (e.g., [15]), a Yamabe soliton is called shrinking, steady, or expanding depending on whether its soliton constant is positive, zero, or negative, respectively.…”

Section: Almost Contact B-metric Manifolds Contact Conformal Transfor...mentioning

confidence: 99%

Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds

Manev

2022

Mathematics

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A Yamabe soliton is defined on an arbitrary almost-contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this manner, manifolds are obtained that belong to one of the main classes of the studied manifolds. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the B-metric on contact distribution. In both cases, explicit five-dimensional examples are given, which are characterized in relation to the results obtained.

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“…As is well known (e.g., [15]), a Yamabe soliton is called shrinking, steady, or expanding depending on whether its soliton constant is positive, zero, or negative, respectively.…”

Section: Almost Contact B-metric Manifolds Contact Conformal Transfor...mentioning

confidence: 99%

Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds

Manev

2022

Mathematics

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“…If λ is a smooth function in (1.2), then it is called almost Yamabe soliton. Alkhaldi et al [1] gave a characterization of almost Yamabe soliton with conformal vector field. Barbosa and Ribeiro [4] gave some rigidity results for Yamabe almost soliton.…”

Section: Introductionmentioning

confidence: 99%

Isometries on almost Ricci–Yamabe solitons

Zosangzuala

Khatri

2022

Arab. J. Math.

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The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere $$S^n(r)$$ S n ( r ) are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h. Next, we studied complete gradient almost Ricci–Yamabe soliton with $$\alpha \ne 0$$ α ≠ 0 and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space $$E^n$$ E n or Euclidean sphere $$S^n.$$ S n . Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results.

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Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Cited by 2 publications

References 22 publications

Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds

Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds

Isometries on almost Ricci–Yamabe solitons

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