JournalsrmiVol. 35, No. 6pp. 1745–1762

On bodies in R5\mathbb R^5 with directly congruent projections or sections

  • M. Angeles Alfonseca

    North Dakota State University, Fargo, USA
  • Michelle Cordier

    Chatham University, Pittsburgh, USA
  • Dmitry Ryabogin

    Kent State University, USA
On bodies in $\mathbb R^5$ with directly congruent projections or sections cover

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Abstract

Let KK and LL be two convex bodies in R5\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,LK,L on certain 3 dimensional subspaces have no symmetries, then K=±LK=\pm L up to a translation. We also prove the corresponding result for sections of star bodies.

Cite this article

M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin, On bodies in R5\mathbb R^5 with directly congruent projections or sections. Rev. Mat. Iberoam. 35 (2019), no. 6, pp. 1745–1762

DOI 10.4171/RMI/1100