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Some rigidity results on shrinking gradient Ricci soliton

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arxiv 2411.06395 v1 pith:DRBF73ZM submitted 2024-11-10 math.DG

classification math.DG
keywords resultsgradientriccishrinkingsolitoncheng-zhoucitemathbb
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abstract

Suppose $(M^n, g, f)$ is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in \cite{Petersen-Wylie,Guan-Lu-Xu}. Using maximum principle, we prove that shrinking gradient Ricci soliton with constant scalar curvature $R=1$ is isometric to a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$, giving a new proof of the main results of Cheng-Zhou \cite{Cheng-Zhou}.

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  1. Rigidity of Five-Dimensional shrinking gradient Ricci solitons

    math.DG 2025-06 conditional novelty 7.0 of 10

    A five-dimensional shrinking gradient Ricci soliton with constant scalar curvature 1 and bounded curvature must be a finite quotient of R^3 × S^2.

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