Projective convexity in $\P^3$ implies Grassmann convexity
B.~Shapiro and M.~Shapiro

In this note  we introduce the notion of Grassmann convexity analogous to
the well-known notion of convexity for curves in real projective spaces. We
show that the curve in $G_{{2,4}}$ osculating to a convex closed curve in
$\bP^3$ is Grassmann-convex. This proves that the tangent developable (i.e.
the hypersurface formed by all tangents) of any convex curve in $\bP^3$ has
the `degree' equal to 4. Here by `degree' of a real projective hypersurface
we mean the maximal total multiplicity of its intersection with a line.