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arXiv · 1906.00444

A gap theorem on complete shrinking gradient Ricci solitons

Shijin Zhang
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Abstract

In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton $(M^{n},g,f)$ with sectional curvature $K(g) 0$ depends only on $n, A$ and $v$, if the scalar curvature $R\leq ε_{n,A,v}$, then $(M,g,f)$ is isometric to the Gaussian soliton $(\mathbb{R}^{n}, g_{E}, \frac{|x|^{2}}{4})$.

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Shijin Zhang. 2019-06-02. A gap theorem on complete shrinking gradient Ricci solitons. https://arxiv.org/abs/1906.00444

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