Recognizing algebraic affine rotation surfaces

Abstract

We investigate the problem of recognizing a generalization of surfaces of revolution appearing in the field of affine differential geometry, namely affine rotation surfaces. By using some notions from affine differential geometry, we determine how to detect whether or not a given implicit algebraic surface is an affine rotation surface. These results generalize some previous results of the authors on surfaces of revolution. As a by-product, we also provide an algorithm to detect whether or not an algebraic surface is an affine sphere, a generalization of Euclidean spheres of interest not only in geometry, but also in other fields.