1996/08/26 by B. Shapiro, Boris Shapiro, Shapiro, B.
Mathematics · #14H50 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #Point processes and geometric inequalities #dg-ga #math.DG #msc:14H50
paper · pdf · doi:10.48550/arxiv.dg-ga/9608007
The usual AMSTeX file, 7 pages, no figures AMSTeX
arxiv created 1996/08/26 · openalex publication_date 1996/08/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given real generic curve \ga: S1→ \Bbb RPn let D_\ga denote the ruled hypersurface in \Bbb RPn consisting of all osculating subspaces to \ga of codimension 2. A curve \ga: S1→ \Bbb RPn is called convex if the total number of its intersection points (counted with multiplicities) with any hyperplane in \Bbb RPn does not exceed n. In this short note we show that for any two convex real projective curves \ga1:S1→\Bbb RPn and \ga2:S1→\Bbb RPn the pairs (\Bbb RPn,D\ga1) and (\Bbb RPn,D\ga2) are homeomorphic answering a question posed by V.Arnold.