A characterization of translated convex bodies
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909743883223040 |
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| author | Morales-Amaya, Efren |
| author_facet | Morales-Amaya, Efren |
| contents | In this work we present a theorem regarding two convex bodies $K_1, K_2\subset \mathbb{R}^{n}$, $n\geq 3$, and two families of sections of them, given by two families of tangent planes of two spheres $S_i\subset \textrm{int}\textrm{ } K_i$, $i=1,2$ such that, for every pair $Π_1$, $Π_2$ of parallel supporting planes of $S_1$, $S_2$, respectively, which are corresponding (this means, that the outer normal vectors of the supporting half spaces determined by the two planes have the same direction), the sections $Π_1\cap K_1$, $Π_2\cap K_2$ are translated, the theorem claims that if $S_1$, $S_2$ have the same radius, the bodies are translated, otherwise, the bodies are also spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of translated convex bodies Morales-Amaya, Efren Metric Geometry In this work we present a theorem regarding two convex bodies $K_1, K_2\subset \mathbb{R}^{n}$, $n\geq 3$, and two families of sections of them, given by two families of tangent planes of two spheres $S_i\subset \textrm{int}\textrm{ } K_i$, $i=1,2$ such that, for every pair $Π_1$, $Π_2$ of parallel supporting planes of $S_1$, $S_2$, respectively, which are corresponding (this means, that the outer normal vectors of the supporting half spaces determined by the two planes have the same direction), the sections $Π_1\cap K_1$, $Π_2\cap K_2$ are translated, the theorem claims that if $S_1$, $S_2$ have the same radius, the bodies are translated, otherwise, the bodies are also spheres. |
| title | A characterization of translated convex bodies |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2407.12310 |