Two Conjectures on Convex Curves
نویسنده
چکیده
Department of Mathematics, University of Oil and Gas (Gubkin) Moscow 117036, Russia [email protected] Department of Mathematics, University of Stockholm S-10691, Sweden, [email protected] Abstra t. In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP3. Namely, we show i) that the tangent developable 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. The question (discussed in [EG1] and [So4]) whether the second conjecture is true in the special case of rational normal curves still remains open.
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¡div class=”moz-text-flowed” style=”font-family: -moz-fixed”¿ ON TWO CONJECTURES CONCERNING CONVEX CURVES
In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP . Namely, we show that i) the tangent developable 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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