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On two conjectures concerning convex curves

V. Sedykh·B. Shapiro
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Abstract

We recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the firdt nontrivial case of curves in RP^3. Namely, we show that i) the tangent developable surface of any convex curve in RP^3 has 'degree' 4 and ii) construct an example of 4 tangent lines to a convex curve in RP^3 such that no real line intersects all four of them.

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V. Sedykh, B. Shapiro. 2005-10-03. On two conjectures concerning convex curves. https://arxiv.org/abs/math/0208218

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