L - Convex - Concave Body in R P 3 Contains a Line
نویسندگان
چکیده
We define a class of L-convex-concave subsets of RP , where L is a projective line in RP . These are sets whose sections by any plane containing L are convex and concavely depend on this plane. We prove a version of Arnold’s conjecture for these sets, namely we prove that each such set contains a line.
منابع مشابه
Convex-concave Body in Rp 3 Contains a Line
We define a class of L-convex-concave subsets of RP 3 , where L is a projective line in RP 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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