Convex-concave body in $\mathbb{R}P^3$ contains a line

Details Convex-concave body in $\mathbb{R}P^3$ contains a line Convex-concave body in $\mathbb{R}P^3$ contains a line

2002-03-19

arxiv.org/abs/math/0203200v1

Mathematics

Differential Geometry

28pp. 37 figures (ups...)

Scientific paper

We 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.

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