2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63608We define a class of $L$-convex-concave subsets of $\mathbb{R}P^3$, where $L$ is a projective line in $\mathbb{R}P^3$. These are sets whose sections by any plane containing $L$ are convex and concavely depend on this plane. We prove a version of Arnold hypothesis for these sets, namely we prove that each such set contains a line.28pp. 37 figures (ups...)Differential GeometryClassical Analysis and ODEs52A30; 26B25, 52A37text