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PreprintCC BY 4.0arXiv

Orientable minimal submanifolds of low index in the sphere

  • Jacob Bernstein
  • Daniel Ketover
Open at sourcePDFDOICite

Abstract

In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only closed and connected (2mβˆ’2)-dimensional orientable minimal submanifolds in π•Š2m of index less than or equal to 2m+1 are the totally geodesic spheres.

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Cite

BibTeXRIS
BibTeX
@misc{bernstein2026orientable,
  title = {{Orientable minimal submanifolds of low index in the sphere}},
  author = {Jacob Bernstein and Daniel Ketover},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23873},
  eprint = {2609.23873},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23873},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Orientable minimal submanifolds of low index in the sphere
AU  - Jacob Bernstein
AU  - Daniel Ketover
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23873
UR  - https://arxiv.org/abs/2609.23873
AB  - In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only closed and connected (2mβˆ’2)-dimensional orientable minimal submanifolds in π•Š^2m of index less than or equal to 2m+1 are the totally geodesic spheres.
ER  -