具有位似截面的凸体

摘要

本文给出了K～+tB(K+tB、K～tB)与K的所有通过原点的k-维截面(2≤k≤n-1}都位似时,K或为以原点为中心的球或为一个椭球的结论.%In this paper, we give the conclusions that a convex body K should be a centered ball when ( K ～+ tB ) ∩S ( ( K + tB ) ∩S, ( K ～ tB ) ∩S, respectively) is homothetic to K ∩ S for each S∈G(n,k), (2≤k≤n- 1).