  For a given real generic curve $\ga: S^1\to \Bbb {RP}^n$ let $D_\ga$ denote
the ruled hypersurface in $\Bbb {RP}^n$ consisting of all osculating subspaces
to $\ga$ of codimension 2. A curve $\ga: S^1\to \Bbb {RP}^n$ is called convex
if the total number of its intersection points (counted with multiplicities)
with any hyperplane in $\Bbb {RP}^n$ does not exceed $n$. In this short note we
show that for any two convex real projective curves $\ga_1:S^1\to\Bbb {RP}^n$
and $\ga_2:S^1\to\Bbb {RP}^n$ the pairs $(\Bbb {RP}^n,D_{\ga_1})$ and $(\Bbb
{RP}^n,D_{\ga_2})$ are homeomorphic answering a question posed by V.Arnold.
