On bodies in R5 with directly congruent projections or sections

• M. Angeles Alfonseca ^[1] ; Michelle Cordier ^[2] ; Dmitry Ryabogin ^[3]
  1. [1] North Dakota State University

     North Dakota State University

     City of Fargo, Estados Unidos

     
  2. [2] Chatham University

     Chatham University

     City of Pittsburgh, Estados Unidos

     
  3. [3] Kent State University

     Kent State University

     City of Kent, Estados Unidos

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 6, 2019, págs. 1745-1762
• Idioma: inglés
• DOI: 10.4171/rmi/1100
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let K and L be two convex bodies in R5 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=±L up to a translation. We also prove the corresponding result for sections of star bodies.