Affine surfaces which admit several affine immersions in \(\mathbb{R}^3\) (Q1029961)

Given a differentiable 2-manifold \(\Sigma\) with a torsion free, Ricci symmetric connection \(\nabla\) and its curvature tensor \(R = R(\nabla)\) with \(\dim\operatorname{Im}R=1\), the author considers the class of all affine immersions that are locally strongly convex Blaschke surfaces in affine 3-space. He gives a local classification of this class modulo some functions that satisfy some ODEs of second order. In case of ovaloids there is a uniqueness result for given data \((\Sigma, \nabla)\) without further assumptions; see the referee's paper [\textit{U. Simon}, Tôhoku Math. J., II. Ser. 44, No.~3, 327--334 (1992; Zbl 0761.53008)].