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<p>We investigate the topology of the compact submanifolds in round spheres that satisfy a lower bound on the Ricci curvature depending only on the length of the mean curvature vector of the immersion. Just in special cases, the limited strength of the assumption allows some strong additional information on the extrinsic geometry of the submanifold.</p>

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Ricci pinched compact submanifolds in spheres

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月30日

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  • Marcos Dajczer,
  • Theodoros Vlachos

摘要

We investigate the topology of the compact submanifolds in round spheres that satisfy a lower bound on the Ricci curvature depending only on the length of the mean curvature vector of the immersion. Just in special cases, the limited strength of the assumption allows some strong additional information on the extrinsic geometry of the submanifold.