Characterizations of the sphere by means of point-projections
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866917235611664384 |
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| author | Jeronimo_Castro, J. Morales-Amaya, E. Hernández, D. J. Verdusco |
| author_facet | Jeronimo_Castro, J. Morales-Amaya, E. Hernández, D. J. Verdusco |
| contents | In this work we prove the following: let $K$ be a convex body in the Euclidean space $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, and let $p\in \mathbb{R}^n$ be a point such that, from each point of $\mathbb{S}^{n-1}$, $K$ looks centrally symmetric and $p$ appears as the center, then $K$ is a ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_04516 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Characterizations of the sphere by means of point-projections Jeronimo_Castro, J. Morales-Amaya, E. Hernández, D. J. Verdusco Metric Geometry In this work we prove the following: let $K$ be a convex body in the Euclidean space $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, and let $p\in \mathbb{R}^n$ be a point such that, from each point of $\mathbb{S}^{n-1}$, $K$ looks centrally symmetric and $p$ appears as the center, then $K$ is a ball. |
| title | Characterizations of the sphere by means of point-projections |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2007.04516 |