On conformal solutions of the Yamabe flow

In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product. By slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient Yamabe solitons possessing certain metric properties on the base of the warped product.2010 Mathematics Subject Classification. 53C21, 53C50, 53C25.

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“…Proof of Theorem 1.3 : We know that a gradient Yamabe soliton (M n , g, ∇h, ρ) with scalar curvature scal g , satisfy (cf. [37]):…”

Section: Proofsmentioning

confidence: 99%

On warped product gradient Yamabe solitons

Tokura

Adriano

Pina

et al. 2019

Journal of Mathematical Analysis and Applications

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“…More clearly, the Yamabe soliton comes from the blow-up procedure along the Yamabe flow, so such solitons have been studied intensively. For further reading we refer [1,4,5,9,17].…”

Section: Introductionmentioning

confidence: 99%

On f-Kenmotsu 3-manifolds with respect to the Schouten–van Kampen connection

Perktaş¹,

Yıldız²

2021

Turk J Math

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“…Yamabe solitons are self-similar solutions for Yamabe flows and they seem to be as singularity models. More clearly, the Yamabe soliton comes from the blow-up procedure along the Yamabe flow, so such solitons have been studied intensively (see [2][3][4][5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

Some remarks on Riemannian submersions admitting an almost Yamabe soliton

Meri̇ç¹

2020

Adıyaman University Journal of Science

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In this paper, we study the Riemannian submersions : MB   whose total manifolds admit an almost Yamabe soliton. Here, we give some necessary conditions for which any fiber of  or B are almost Yamabe soliton or Yamabe soliton. Also, we calculate the scalar curvatures of any fiber and B and using them, we present the relations between the scalar curvatures of them and obtain some characterizations of such a soliton (that is, shrinking, steady or expanding).

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On conformal solutions of the Yamabe flow

Cited by 90 publications

References 18 publications

On warped product gradient Yamabe solitons

On warped product gradient Yamabe solitons

On f-Kenmotsu 3-manifolds with respect to the Schouten–van Kampen connection

Some remarks on Riemannian submersions admitting an almost Yamabe soliton

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