Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Martins, Gustavo
Institution: Instituto Nacional de Matemática Pura e Aplicada
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213602869