Duality of subanalytic sets

Details Duality of subanalytic sets Duality of subanalytic sets

1997-06-10

arxiv.org/abs/dg-ga/9706007v2

Mathematics

Differential Geometry

LaTex, 20 pages, submitted to Geometriae Dedicata

Scientific paper

We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ 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.

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