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arXiv · 2411.10712

Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

Fengjiang Li·Jianyu Ou·Yuanyuan Qu·Guoqiang Wu
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Abstract

Let $(M, g, f)$ be a $5$-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \lambda g$, where $\text{Ric}$ is the Ricci tensor and $\nabla^2f$ is the Hessian of the potential function $f$. We prove that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^3$ if $M$ has constant scalar curvature $R=3 \lambda$.

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Fengjiang Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu. 2024-11-16. Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature. https://arxiv.org/abs/2411.10712

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