On the affine theory of the Peterson correspondence between hypersurfaces (Q1897917)

The Peterson correspondence between hypersurfaces in a real vector space has an affine rather than metric nature. More precisely, this nature pertains to relative geometry: for example, and for a couple of hypersurfaces in Peterson correspondence, the present article considers the connections induced on these hypersurfaces by the vector field determined by their corresponding points. The author treats the relations and properties of these connections and formulates the conditions under which the given hypersurfaces are homothetic.