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Topological and spectral rigidity of hypersurface Zoll manifolds

  • Gustavo Martins
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Abstract

We show that manifolds admitting Zoll families of minimal hypersurfaces are diffeomorphic to π•Šn or to ℝℙn, and we characterize their Zoll families in both cases. Then, we prove that a metric on ℝℙ3 is surface Zoll if and only if its projective widths are all equal. Our last result asserts that a closed surface with the first four widths equal to 2Ο€ is isometric to ℝℙ2 with its constant curvature one metric.

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Cite

BibTeXRIS
BibTeX
@misc{martins2026topological,
  title = {{Topological and spectral rigidity of hypersurface Zoll manifolds}},
  author = {Gustavo Martins},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20689},
  eprint = {2609.20689},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20689},
}
RIS
TY  - UNPB
TI  - Topological and spectral rigidity of hypersurface Zoll manifolds
AU  - Gustavo Martins
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.20689
UR  - https://arxiv.org/abs/2609.20689
AB  - We show that manifolds admitting Zoll families of minimal hypersurfaces are diffeomorphic to π•Š^n or to ℝℙ^n, and we characterize their Zoll families in both cases. Then, we prove that a metric on ℝℙ^3 is surface Zoll if and only if its projective widths are all equal. Our last result asserts that a closed surface with the first four widths equal to 2Ο€ is isometric to ℝℙ^2 with its constant curvature one metric.
ER  -