Affine rotational surfaces with vanishing affine curvature (Q1882454)

In affine differential geometry there exists 4 different types of rotation surfaces. A rotation surface is called proper if the axis is a proper line: in which case the parallel curves can be ellipses, hyperbolas or parabolas. The 4th type happens if the axis is the line at infinity. In all cases, a rotation surface is determined by a single function \(r\) of 1-variable. The author determines in each case the expression of the affine invariants in terms of the function \(r\) and its derivatives. From this, he obtains a classification of all affine rotation surfaces for which the Gauss-Kronecker curvature vanishes, i.e. for which the determinant of the affine shape operator vanishes.