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<p>We investigate the topology of the compact hypersurfaces in round spheres focusing on those with the Ricci curvature satisfying an appropriate bound determined solely by the mean curvature of the submanifold. In this paper, the application of the Bochner technique yields more robust results compared to those presented in [<CitationRef CitationID="CR2">2</CitationRef>] for submanifolds that lay in any codimension.</p>

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Ricci pinched compact hypersurfaces in spheres

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月16日

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  • M. Dajczer,
  • M. I. Jimenez,
  • Th. Vlachos

摘要

We investigate the topology of the compact hypersurfaces in round spheres focusing on those with the Ricci curvature satisfying an appropriate bound determined solely by the mean curvature of the submanifold. In this paper, the application of the Bochner technique yields more robust results compared to those presented in [2] for submanifolds that lay in any codimension.