Affine semiparallel surfaces with constant Pick invariant (Q2574437)

Let \(M\) be a non-degenerate (unimodular) Blaschke surface in affine 3-space with induced connection \(\nabla\), associated curvature tensor \(R\) and affine shape operator \(S\). \(M\) is called \textit{semiparallel} if \(R(X,Y)S = 0.\) The authors classify such surfaces under the additional assumption that the Pick invariant is constant: they are either affine spheres (in this case the surfaces are exactly the affine spheres with constant curvature Blaschke metric [see \textit{U. Simon}, Differ. Geom. Appl. 1, No. 2, 123--132 (1991; Zbl 0784.53002)]) or affine ruled surfaces with vanishing affine mean curvature.