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arXiv · 2407.02755

Convex bodies with pairs of sections associated by reflections

Efren Morales-Amaya
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Abstract

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 $K_2$.

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Efren Morales-Amaya. 2024-07-03. Convex bodies with pairs of sections associated by reflections. https://doi.org/10.1007/s13366-025-00806-w

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