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arXiv · 1801.08987

On bodies in $\mathbb{R}^5$ with directly congruent projections or sections

M. Angeles Alfonseca·Michelle Cordier·Dmitry Ryabogin
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Abstract

Let $K$ and $L$ be two convex bodies in ${\mathbb R^5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rotational symmetries, and the projections of $K,L$ on certain 3 dimensional subspaces have no symmetries, then $K=\pm L$ up to a translation. We also prove the corresponding result for sections of star bodies.

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M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin. 2018-01-26. On bodies in $\mathbb{R}^5$ with directly congruent projections or sections. https://arxiv.org/abs/1801.08987

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