1997/06/10 by F. Pointet, Francois Pointet, Pointet, Francois
Mathematics · #32B20 (primary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG #msc:32B20
paper · pdf · doi:10.48550/arxiv.dg-ga/9706007
LaTex, 20 pages, submitted to Geometriae Dedicata
openalex publication_date 1997/06/10 · arxiv created 1997/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the link between a compact hypersurface in ¶n+1 and the set of all its tangent planes. In this context, we identify ¶n+1 to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise to a kind of duality which has already been studied Bruce and Romerro-Fuster, and relates a hypersurface to the set of its tangent planes. But in these papers the dual, in this sense, of the set of tangent planes of a hypersurface was not defined and iteration of the procedure was not possible. Therefore we extend this type of duality to more general sets and achieve a procedure which can be iterated and gives in fact an involution.