What principle underlies the vanishing curvature?
Curvature cancellation conjecture
¥(When an elastic flat sheet of elastic thickness h is constrained by normal forces that are unbalanced except over distances R >> h, the shape converges pointwise as h/R¨0 to an a developable surface with an uncurved director through every point.  For certain choices of constraint forces, the directors converge to a point, thus forming a developable cone.)
¥If part of a d-cone is constrained (with nonzero normal force)  to follow a curve that imposes nonzero curvature perpendicular to the director lines, then the Àmean curvature averaged over this curve vanishes when h/R¨0 ? .
The true conditions for when mean curvature vanishes are not known.