A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

Fuente: arXiv
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Main Authors: Wang, Chen, Wu, Guoqiang
Format: Preprint
Published: 2026
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author Wang, Chen
Wu, Guoqiang
author_facet Wang, Chen
Wu, Guoqiang
contents Let $(M^4, g, f)$ be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \frac{1}{2}g$. If its scalar curvature is $1$, Cheng-Zhou \cite{Cheng-Zhou} proved that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$. In this note we present an alternative proof by analyzing the asymptotic geometry at infinity.
format Preprint
id arxiv_https___arxiv_org_abs_2604_26163
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
Wang, Chen
Wu, Guoqiang
Differential Geometry
Analysis of PDEs
Let $(M^4, g, f)$ be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \frac{1}{2}g$. If its scalar curvature is $1$, Cheng-Zhou \cite{Cheng-Zhou} proved that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$. In this note we present an alternative proof by analyzing the asymptotic geometry at infinity.
title A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
topic Differential Geometry
Analysis of PDEs
url https://arxiv.org/abs/2604.26163