gradient soliton
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2020 ◽  
Vol 31 (06) ◽  
pp. 2050044
Author(s):  
Pak Tung Ho

In this paper, we study the Ricci–Bourguignon flow of all locally homogenous geometries on closed three-dimensional manifolds. We also consider the evolution of the Yamabe constant under the Ricci–Bourguignon flow. Finally, we prove some results for the Bach-flat shrinking gradient soliton to the Ricci–Bourguignon flow.


Author(s):  
Yadab Chandra Mandal ◽  
Shyamal Kumar Hui

The Yamabe soliton is a special soliton of Yamabe flow obtained by R. S. Hamilton, which was formulated due to Yamabe formula introduced by H. Yamabe in 1960. Recently Cao, Sun and Zhang introduced Yamabe gradient soliton. In this paper, the existence of Yamabe gradient solitons on 4-dimensional Riemannian manifold are ensured by some interesting examples.


2012 ◽  
Vol 14 (06) ◽  
pp. 1250045 ◽  
Author(s):  
GIOVANNI CATINO ◽  
CARLO MANTEGAZZA ◽  
LORENZO MAZZIERI

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product ℝ × Nn-1, or globally conformally equivalent to the Euclidean space ℝn or to the round sphere 𝕊n. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.


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