2023/08/05 by Aguilar-Arteaga, Victor A., Ayala-Figueroa, Rafael Iván, Jerónimo-Castro, Jesús +1
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2308.02956
Let K and L be two convex bodies in \mathbb Rn, n≥ 3, with L⊂ int K. In this paper we prove the following result: if every two parallel chords of K, supporting L have the same length, then K and L are homothetic and concentric ellipsoids. We also prove a similar theorem when instead of parallel chords we consider concurrent chords. We may also replace, in both theorems, supporting chords of L by supporting sections of constant width. In the last section we also prove similar theorems where we consider projections instead of sections.