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Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature

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  • Yawei Chu
  • Dehe Li
  • Jundong Zhou

Abstract

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

Suggested Citation

  • Yawei Chu & Dehe Li & Jundong Zhou, 2021. "Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-8, August.
    • Handle: RePEc:hin:jnlamp:4907963
    DOI: 10.1155/2021/4907963
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