On affine hypersurfaces with parallel second fundamental form. (Q1872827)

Consider an \(n\)-dimensional, non-degenerate hypersurface in real affine space. The Blaschke metric \(h\) and the cubic Pick form \(C\) form a fundamental system of invariants of the hypersurface with respect to the unimodular transformation group. The author states and proves a classification result for non-degenerate hypersurfaces with parallel cubic form, \(\nabla(h)C\equiv0\), where \(\nabla(h)\) denotes the Levi-Civita connection of the metric \(h\). This classification is already known; for this and earlier results see the paper of \textit{N. Bokan, K. Nomizu} and \textit{U. Simon} [ ibid. 42, 101--108 (1990; Zbl 0696.53006)]. The paper of Bokan et al. contains more general classification results (loc. cit.,Theorem 1).