{"ID":23629743,"CreatedAt":"2026-09-18T07:04:54.147703138Z","UpdatedAt":"2026-09-18T07:04:54.147703138Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20689","arxiv_id":"2609.20689","title":"Topological and spectral rigidity of hypersurface Zoll manifolds","abstract":"We show that manifolds admitting Zoll families of minimal hypersurfaces are diffeomorphic to $\\mathbb{S}^{n}$ or to $\\mathbb{R}\\mathbb{P}^{n}$, and we characterize their Zoll families in both cases. Then, we prove that a metric on $\\mathbb{R}\\mathbb{P}^3$ 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 $2π$ is isometric to $\\mathbb{R}\\mathbb{P}^2$ with its constant curvature one metric.","short_abstract":"We show that manifolds admitting Zoll families of minimal hypersurfaces are diffeomorphic to $\\mathbb{S}^{n}$ or to $\\mathbb{R}\\mathbb{P}^{n}$, and we characterize their Zoll families in both cases. Then, we prove that a metric on $\\mathbb{R}\\mathbb{P}^3$ is surface Zoll if and only if its projective widths are all equ...","url_abs":"https://arxiv.org/abs/2609.20689","url_pdf":"https://arxiv.org/pdf/2609.20689v1","authors":"[\"Gustavo Martins\"]","published":"2026-09-17T16:56:22Z","proceeding":"math.DG","tasks":"[\"math.DG\"]","methods":"[]","has_code":false}