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PreprintarXiv licencearXiv

Rigidity of Minimal Submanifolds in Spheres of Higher Codimension

  • Li Lei
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Abstract

We investigate Chern's conjecture for minimal submanifolds of higher codimension in the unit sphere. We establish two integral inequalities for closed minimal submanifolds. Then we obtain a new rigidity theorem under a pinching condition on the squared norm of the second fundamental form.

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Cite

BibTeXRIS
BibTeX
@misc{lei2026rigidity,
  title = {{Rigidity of Minimal Submanifolds in Spheres of Higher Codimension}},
  author = {Li Lei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04393},
  eprint = {2609.04393},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04393},
}
RIS
TY  - UNPB
TI  - Rigidity of Minimal Submanifolds in Spheres of Higher Codimension
AU  - Li Lei
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04393
UR  - https://arxiv.org/abs/2609.04393
AB  - We investigate Chern's conjecture for minimal submanifolds of higher codimension in the unit sphere. We establish two integral inequalities for closed minimal submanifolds. Then we obtain a new rigidity theorem under a pinching condition on the squared norm of the second fundamental form.
ER  -