Convex bodies with pairs of sections associated by reflections
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912863310839808 |
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| author | Morales-Amaya, Efren |
| author_facet | Morales-Amaya, Efren |
| contents | In this work we prove that if for a pair of convex bodies $K_1, K_2 \subset \mathbb{R}^n$, $n \geq 3$, there exists a hyperplane $H$ and two distinct points $p_1$ and $p_2$ in $\mathbb{R}^n \setminus H$ such that for every $(n-2)$-plane $M \subset H$, there exists a reflection mapping the hypersection of $K_1$ defined by $\mathrm{aff}\{p_1, M\}$ onto the hypersection of $K_2$ defined by $\mathrm{aff}\{p_2, M\}$, then there exists a reflection which maps $K_1$ onto $K_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex bodies with pairs of sections associated by reflections Morales-Amaya, Efren Metric Geometry In this work we prove that if for a pair of convex bodies $K_1, K_2 \subset \mathbb{R}^n$, $n \geq 3$, there exists a hyperplane $H$ and two distinct points $p_1$ and $p_2$ in $\mathbb{R}^n \setminus H$ such that for every $(n-2)$-plane $M \subset H$, there exists a reflection mapping the hypersection of $K_1$ defined by $\mathrm{aff}\{p_1, M\}$ onto the hypersection of $K_2$ defined by $\mathrm{aff}\{p_2, M\}$, then there exists a reflection which maps $K_1$ onto $K_2$. |
| title | Convex bodies with pairs of sections associated by reflections |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2407.02755 |