# On strict inclusions in hierarchies of convex bodies - Mathematics > Metric Geometry

Abstract: Let $\mathcal I k$ be the class of convex $k$-intersection bodies in$\mathbb{R}^n$ in the sense of Koldobsky and $\mathcal I k^m$ be the class ofconvex origin-symmetric bodies all of whose $m$-dimensional central sectionsare $k$-intersection bodies. We show that 1 $\mathcal I k^m ot\subset\mathcal I k^{m+1}$, \$k+3\le m