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<p>In this paper, the authors investigate the geometric rigidity of Riemannian manifolds under suitable curvature restrictions. The authors first prove a new gap theorem for the Ricci curvature of compact locally conformally flat Riemannian manifolds. Subsequently, the authors consider the Riemannian manifolds with the Cotton tensor <i>C</i> satisfying div <i>C</i> = 0 and prove some integral curvature pinching theorems.</p>

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The New Gap Theorem for Certain Riemannian Manifolds

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Juan Li,
  • Hongwei Xu,
  • Entao Zhao

摘要

In this paper, the authors investigate the geometric rigidity of Riemannian manifolds under suitable curvature restrictions. The authors first prove a new gap theorem for the Ricci curvature of compact locally conformally flat Riemannian manifolds. Subsequently, the authors consider the Riemannian manifolds with the Cotton tensor C satisfying div C = 0 and prove some integral curvature pinching theorems.