Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature

Yawei Chu, Dehe Li and Jundong Zhou

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: Let (Mn, g, f) be a complete gradient shrinking Ricci soliton of dimension n ≥ 3. In this paper, we study the rigidity of (Mn, g, f) with pointwise pinching curvature and obtain some rigidity results. In particular, we prove that every n‐dimensional gradient shrinking Ricci soliton (Mn, g, f) is isometric to ℝn or a finite quotient of Sn under some pointwise pinching curvature condition. The arguments mainly rely on algebraic curvature estimates and several analysis tools on (Mn, g, f), such as the property of f‐parabolic and a Liouville type theorem.

Date: 2021
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https://doi.org/10.1155/2021/4907963

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:4907963

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