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

Chen Wang; Guoqiang Wu

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arXiv · 2604.26163

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

Chen Wang·Guoqiang Wu

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Abstract

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.

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Chen Wang, Guoqiang Wu. 2026-04-28. A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature. https://arxiv.org/abs/2604.26163

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