Inductive schemes for the complete classification of affine hypersurfaces with parallel second fundamental form

Abstract

We present in this article inductive schemes that allow to classify all those affine hypersurfaces with affine normal parallel second fundamental (cubic) form, for every possible dimensional case greater or equal than two. The solution proposed is a follow up to previous works on the same topic by this author and it uses, firstly, the reduction of the problem, eminently geometric, to the classification of a certain class of solutions to an equation of Monge-Ampere type. Then it is applied the so-called “method of algorithmic sequence of coordinate changes”, in order to achieve the latter.