Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in paracontact geometry

De, Krishnendu; De, Uday Chand

doi:10.2989/16073606.2020.1799882

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…Geodesic mappings of these spaces are studied in [27]. Also [2] treated spaces with generalized φ(Ric) vector fields. Substituting (4.4) into (4.3), we obtain…”

Section: Pseudo-riemannian Spaces With Differential Conditions Imposed On the Supplementary Tensormentioning

confidence: 99%

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

Кіосак¹,

Пришляк

Lesechko

2021

PIGC

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В роботі досліджуються два псевдоріманових простори, які мають спільні геодезичні лінії. Вимагається виконання умов алгебраїчного та диференціального характеру на тензор Рімана одного з них. А операція опускання індексів та обчислення коваріантної похідної здійснюється відносно метрики та об'єктів зв'язності іншого простору. Для досліджень використовується спеціальний допоміжний тензор. Доведено, що виконання додаткових умов приводить до просторів, що не допускають нетривіальних геодезичних відображень, або простори належать до еквідістантних просторів. Використовуються тензорні методи без обмежень на знак метрики.

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“…Geodesic mappings of these spaces are studied in [27]. Also [2] treated spaces with generalized φ(Ric) vector fields. Substituting (4.4) into (4.3), we obtain…”

Section: Pseudo-riemannian Spaces With Differential Conditions Imposed On the Supplementary Tensormentioning

confidence: 99%

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

Кіосак¹,

Пришляк

Lesechko

2021

PIGC

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“…It is nothing more than a generalized quasi-Yamabe gradient soliton (GQYGS) (see [4,5]). Several authors have thoroughly investigated AQYS and QYGS in [6][7][8][9][10][11][12][13]. Definition 2.…”

Section: Definition 1 An Almost Quasi-yamabe Solitons (Aqys) Onmentioning

confidence: 99%

A Note on $LP$ -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

Yadav¹,

Suthar

Shimelis

2021

Journal of Mathematics

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We categorize almost quasi-Yamabe solitons on LP -Sasakian manifolds and their CR -submanifolds whose potential vector field is torse-forming, admitting a generalized symmetric metric connection of type α , β . Finally, a nontrivial example is provided to confirm some of our results.

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“…In [3,10,11] and also by others, some important results on Yamabe solitons have been studied. In [12], the authors studied Yamabe and gradient Yamabe solitons in perfect fluid spacetimes.…”

Section: Introductionmentioning

confidence: 96%

Perfect Fluid Spacetimes and Gradient Solitons

Syied

et al. 2022

J Nonlinear Math Phys

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In this article, we investigate perfect fluid spacetimes equipped with concircular vector field. At first, in a perfect fluid spacetime admitting concircular vector field, we prove that the velocity vector field annihilates the conformal curvature tensor. In addition, in dimension 4, we show that a perfect fluid spacetime is a generalized Robertson–Walker spacetime with Einstein fibre. It is proved that if a perfect fluid spacetime furnished with concircular vector field admits a second order symmetric parallel tensor P, then either the equation of state of the perfect fluid spacetime is characterized by $$p=\frac{3-n}{n-1} \sigma $$ p = 3 - n n - 1 σ , or the tensor P is a constant multiple of the metric tensor. Finally, The perfect fluid spacetimes with concircular vector field whose Lorentzian metrics are Ricci soliton, gradient Ricci soliton, gradient Yamabe solitons, and gradient m -quasi Einstein solitons, are characterized.

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Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in paracontact geometry

Cited by 9 publications

References 15 publications

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

A Note on $LP$ -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

Perfect Fluid Spacetimes and Gradient Solitons

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Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in paracontact geometry

Cited by 9 publications

References 15 publications

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

A Note on LP -Sasakian Manifolds with Almost Quasi-Yamabe Solitons

Perfect Fluid Spacetimes and Gradient Solitons

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A Note on $LP$ -Sasakian Manifolds with Almost Quasi-Yamabe Solitons