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arXiv · 2007.04516

Characterizations of the sphere by means of point-projections

J. Jeronimo_Castro·E. Morales-Amaya·D. J. Verdusco Hernández
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Abstract

In this work we prove the following: let $K$ be a convex body in the Euclidean space $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, and let $p\in \mathbb{R}^n$ be a point such that, from each point of $\mathbb{S}^{n-1}$, $K$ looks centrally symmetric and $p$ appears as the center, then $K$ is a ball.

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J. Jeronimo_Castro, E. Morales-Amaya, D. J. Verdusco Hernández. 2020-07-09. Characterizations of the sphere by means of point-projections. https://doi.org/10.1007/s00454-024-00712-3

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