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arXiv · 2108.01732

A characterization of centrally symmetric convex bodies in terms of visual cones

E. Morales-Amaya·J. Jerónimo-Castro·D. J. Verdusco-Hernández
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Abstract

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.

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E. Morales-Amaya, J. Jerónimo-Castro, D. J. Verdusco-Hernández. 2021-08-03. A characterization of centrally symmetric convex bodies in terms of visual cones. https://doi.org/10.1515/advgeom-2022-0006

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