2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95333We 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.AMSTEX, 15 pages, 3 eps pictures. to appear in Int. J. MathAlgebraic Geometry53A04text