On bodies with congruent sections or projections

Ning Zhang

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arXiv · 1711.10445

On bodies with congruent sections or projections

Ning Zhang

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Abstract

In this paper, we construct two convex bodies $K$ and $L$ in $\mathbb{R}^n$, $n\geq 3$, such that their projections $K|H$, $L|H$ onto every subspace $H$ are congruent, but nevertheless, $K$ and $L$ do not coincide up to a translation or a reflection in the origin. This gives a negative answer to an old conjecture posed by Nakajima and S\"uss.

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Ning Zhang. 2017-11-28. On bodies with congruent sections or projections. https://arxiv.org/abs/1711.10445

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