2014/12/08 by M. Angeles Alfonseca, Alfonseca, M. Angeles, Michelle Cordier +3
Mathematics · #52A20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #math.CA #math.MG #msc:52A20
paper · pdf · doi:10.48550/arxiv.1412.2727
29 pages, 4 figures
arxiv created 2015/09/29 · arxiv updated 2015/09/30
Let K and L be two convex bodies in \mathbb R4, such that their projections onto all 3-dimensional subspaces are directly congruent. We prove that if the set of diameters of the bodies satisfy an additional condition and some projections do not have certain symmetries, then K and L coincide up to translation and an orthogonal transformation. We also show that an analogous statement holds for sections of star bodies, and prove the n-dimensional versions of these results.