A characterization of centrally symmetric convex bodies in terms of visual cones
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915763815710720 |
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| author | Morales-Amaya, E. Jerónimo-Castro, J. Verdusco-Hernández, D. J. |
| author_facet | Morales-Amaya, E. Jerónimo-Castro, J. Verdusco-Hernández, D. J. |
| contents | In this work we prove the following result: Let $K$ be a strictly convex body in the Euclidean space $\mathbb{R}^n, n\geq 3$, and let $L$ be a hypersurface, which is the image of an embedding of the sphere $\mathbb{S}^{n-1}$, such that $K$ is contained in the interior of $L$. Suppose that, for every $x\in L$, there exists $y\in L$ such that the support double-cones of $K$ with apexes at $x$ and $y$, differ by a translation. Then $K$ and $L$ are centrally symmetric and concentric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01732 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A characterization of centrally symmetric convex bodies in terms of visual cones Morales-Amaya, E. Jerónimo-Castro, J. Verdusco-Hernández, D. J. Metric Geometry In this work we prove the following result: Let $K$ be a strictly convex body in the Euclidean space $\mathbb{R}^n, n\geq 3$, and let $L$ be a hypersurface, which is the image of an embedding of the sphere $\mathbb{S}^{n-1}$, such that $K$ is contained in the interior of $L$. Suppose that, for every $x\in L$, there exists $y\in L$ such that the support double-cones of $K$ with apexes at $x$ and $y$, differ by a translation. Then $K$ and $L$ are centrally symmetric and concentric. |
| title | A characterization of centrally symmetric convex bodies in terms of visual cones |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2108.01732 |